Let X(1) = {X(1)(s), s ∈ R+} and X(2) = {X(2)(t), t ∈ R+} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample pat...Let X(1) = {X(1)(s), s ∈ R+} and X(2) = {X(2)(t), t ∈ R+} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X (1) and X (2) are studied. More gener-ally, let E1, E2?(0,∞) and F ?Rd be Borel sets. A necessary condition and a suffcient condition for P{X(1)(E1)∩X(2)(E2)∩F 6=?}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space (R+× R+× Rd,ρb), whereρb is an unsymmetric metric defined in R+× R+× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.展开更多
The segregation of thermal diffusion salt bath chromizing process was analyzed. The experimental chromizing ingredients were prepared by the four groups A, B, C, and D. In order to study the segregation status of this...The segregation of thermal diffusion salt bath chromizing process was analyzed. The experimental chromizing ingredients were prepared by the four groups A, B, C, and D. In order to study the segregation status of this case, the cooling molten salt in the crucible was removed by drilling from the heart core of molten salt. The core of molten salt was analyzed by X-ray fluorescence spectroscopy and XRD. Through the analysis, we can conclude that the Cr element deposited in the bottom was 4.51 times than the top. Chloride added to the molten salt will reduce segregation. Meantime we proposed some measures to overcome the segregation problem.展开更多
This paper is concerned with a control problem of a diffusion process with the help of static mesh sensor networks in a certain region of interest and a team of networked mobile actuators carrying chemical neutralizer...This paper is concerned with a control problem of a diffusion process with the help of static mesh sensor networks in a certain region of interest and a team of networked mobile actuators carrying chemical neutralizers.The major contribution of this paper can be divided into three parts:the first is the construction of a cyber-physical system framework based on centroidal Voronoi tessellations(CVTs),the second is the convergence analysis of the actuators location,and the last is a novel proportional integral(PI)control method for actuator motion planning and neutralizing control(e.g.,spraying)of a diffusion process with a moving or static pollution source,which is more effective than a proportional(P)control method.An optimal spraying control cost function is constructed.Then,the minimization problem of the spraying amount is addressed.Moreover,a new CVT algorithm based on the novel PI control method,henceforth called PI-CVT algorithm,is introduced together with the convergence analysis of the actuators location via a PI control law.Finally,a modified simulation platform called diffusion-mobile-actuators-sensors-2-dimension-proportional integral derivative(Diff-MAS2D-PID)is illustrated.In addition,a numerical simulation example for the diffusion process is presented to verify the effectiveness of our proposed controllers.展开更多
Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x(L^κB) 〈∞ is pr...Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x(L^κB) 〈∞ is proved.展开更多
The cone condition for x to be tegular for B under the elliptic diffusionprocess was proved. We also gave a necessary and sufficient condition for 0 to be regular for thornunder the elliptic diffusion process.
The entropy production rate of stationary minimal diffusion processes with smooth coefficients is calculated. As a byproduct, the continuity of paths of the minimal diffusion processes is discussed, and that the point...The entropy production rate of stationary minimal diffusion processes with smooth coefficients is calculated. As a byproduct, the continuity of paths of the minimal diffusion processes is discussed, and that the point at infinity is absorbing is proved.展开更多
The hedging problem for insiders is very important in the financial market.The locally risk minimizing hedging was adopted to solve this problem.Since the market was incomplete,the minimal martingale measure was chose...The hedging problem for insiders is very important in the financial market.The locally risk minimizing hedging was adopted to solve this problem.Since the market was incomplete,the minimal martingale measure was chosen as the equivalent martingale measure.By the F-S decomposition,the expression of the locally risk minimizing strategy was presented.Finally,the local risk minimization was applied to index tracking and its relationship with tracking error variance (TEV)-minimizing strategy was obtained.展开更多
In this paper, we propose a Gasser-Müller type spot volatility estimator (abbreviated as GM type estimator) for diffusion process, which is weighted by integrals, it is different from the kernel spot volatility e...In this paper, we propose a Gasser-Müller type spot volatility estimator (abbreviated as GM type estimator) for diffusion process, which is weighted by integrals, it is different from the kernel spot volatility estimator discussed by Kristensen (2010). Under more general conditions, the asymptotic unbiasedness and the asymptotic normality of the GM type estimator are derived. The simulation results show that the GM type spot volatility estimator has good estimation effect, and its mean square error tends to be less than that of the kernel spot volatility estimator discussed by Kristensen (2010), so it provides a selection method for estimating the spot volatility in high frequency data environment.展开更多
Grain boundary diffusion process(GBDP)was first proposed for sintered Nd-Fe-B magnets to achieve the high utilization efficiency of heavy rare earth elements.Recent success of fabricating high performance nanocomposit...Grain boundary diffusion process(GBDP)was first proposed for sintered Nd-Fe-B magnets to achieve the high utilization efficiency of heavy rare earth elements.Recent success of fabricating high performance nanocomposite magnets by GBDP indicates that this method also exerts huge applicable potential on hot-deformed Nd-Fe-B magnets.In this review,the development and magnetic property enhancement mechanisms of different diffusion methods proposed on hot-deformed magnets were thoroughly elucidated.Moreover,the improve room for further property enhancement and the accompanying problems of GBDP on hot-deformed magnets are also discussed in this article.展开更多
The rare earth-iron-boron magnets based on high abundance rare earths(REs)show potential for costeffective permanent magnets but their hard magnetic properties have to be greatly improved.The grain boundary diffusion ...The rare earth-iron-boron magnets based on high abundance rare earths(REs)show potential for costeffective permanent magnets but their hard magnetic properties have to be greatly improved.The grain boundary diffusion process(GBDP)is known as an effective way to improve the coercivity of Nd-Fe-B magnets,however,the conventional diffusion method faces a challenge for Ce-based magnets since there is no enough continuous GB layer as the diffusion channel.Here,a two-step(Nd-Cu doping followed by Nd-Cu diffusion)GBDP was introduced for hot deformed(Ce,La,Y)-Fe-B magnet,and the excellent magnetic properties ofμ0Hc=0.63 T,μ0Mr=0.68 T,and(BH)max=72.4 kJ/m^(3)were achieved.The Nd-Cu doping helps the formation of RE-rich GB layer,and then it acts as the diffusion channel for increasing the ef-ficiency of the subsequent Nd-Cu diffusion and results in the increased volume fraction of continuously distributed GB phase,whose paramagnetism was verified by 57Fe Mössbauer spectrometry.Those paramagnetic GB phases help to form the discontinuous domain walls,as observed by Lorentz transmission electron microscopy,and break the magnetic exchange coupling of RE2Fe14B grains.It thus contributes to the coercivity enhancement of the hot deformed magnet with two-step diffusion,which is further proved by micromagnetic simulation.This study proposes a potential technique to prepare anisotropic hot deformed(Ce,La,Y)-Fe-B magnet with high cost-performance.展开更多
For any N≥2 andα=(α1…,αN+1)∈(0,∞)^N+1,letμa^(N)be the Dirichlet distribution with parameterαon the set△(N):={x^μa∈[0,1]^N:∑1≤i≤N^xi≤1}.The multivariate Dirichlct diffusion is associated with the Dirich...For any N≥2 andα=(α1…,αN+1)∈(0,∞)^N+1,letμa^(N)be the Dirichlet distribution with parameterαon the set△(N):={x^μa∈[0,1]^N:∑1≤i≤N^xi≤1}.The multivariate Dirichlct diffusion is associated with the Dirichlet formεa^(N)(f,f):=∑n=i^N∫△(N)(1-∑1≤i≤N^xi)xn(Эnf)^2(x)μα^(N)(dx)with Domain D(εa^(N))being the closure of C^1(△^(N)).We prove the Nash inequalityμa^(N)(f^2)≤Cεa^(N)(f,f)^p/(p+1)μa^(N)(|f|)^2/(p+1),f∈D(εa^(N)),μa^(N)(f)=0 for some constant C>0 and p=(aN+1-1)++∑i^N=11∨(2ai),where the constant p is sharp when max1≤i≤N ai≤1/2 and aN+1≥1.This Nash inequality also holds for the corresponding Fleming-Viot process.展开更多
The goal of this paper is to study large deviations for estimator and score function of some time inhomogeneous diffusion process. Large deviation in the non-steepness case with explicit rate functions is obtained by ...The goal of this paper is to study large deviations for estimator and score function of some time inhomogeneous diffusion process. Large deviation in the non-steepness case with explicit rate functions is obtained by using parameter-dependent change of measure.展开更多
We consider the asymptotic property of the diffusion processes with Markovian switching. For a general case, we prove a large deviation principle for empirical measures of switching diffusion processes with small para...We consider the asymptotic property of the diffusion processes with Markovian switching. For a general case, we prove a large deviation principle for empirical measures of switching diffusion processes with small parameters.展开更多
In this paper,a class of reaction diffusion processes with general reaction rates is studied.A necessary and sufficient condition for the reversibility of this calss of reaction diffusion processes is given,and then t...In this paper,a class of reaction diffusion processes with general reaction rates is studied.A necessary and sufficient condition for the reversibility of this calss of reaction diffusion processes is given,and then the ergodicity of these processes is proved.展开更多
In this paper,we define the generalized diffusion operator L=d/dMd/dS for two suitable measures on the line,which includes the generators of the birth-death processes,the one-dimensional diffusion and the gap diffusio...In this paper,we define the generalized diffusion operator L=d/dMd/dS for two suitable measures on the line,which includes the generators of the birth-death processes,the one-dimensional diffusion and the gap diffusion among others.Via the standard resolvent approach,the associated generalized diffusion processes are constructed.展开更多
Two typical ARCH models: the ASDARCH model and the APARCH model are analyzed. Let Y k and σ 2 k denote the log returns and the volatility. When the time interval h goes to zero, (Y k,σ 2 k), as a dis...Two typical ARCH models: the ASDARCH model and the APARCH model are analyzed. Let Y k and σ 2 k denote the log returns and the volatility. When the time interval h goes to zero, (Y k,σ 2 k), as a discrete time Markov chain system, weakly converges to a continuous time diffusion process. The continuous time approximation of the ASDARCH model is done using two different methods. With some transformation, these two results are equivalent to high frequency data. The continuous time approximation of the APARCH model is obtained by a different procedure.展开更多
Let τ_D denote the lifetime of a diffusion process on domain DR^d. This paper presents a sufficient condition for the exponential moment of τ_D to be finite. Here, both of the domain and the diffusion operator are g...Let τ_D denote the lifetime of a diffusion process on domain DR^d. This paper presents a sufficient condition for the exponential moment of τ_D to be finite. Here, both of the domain and the diffusion operator are general. As an application, the main result of Gao(1995) for conditioned diffusions is improved on.展开更多
In the present paper we consider the small random perturbations of one-dimensional diffosion processes. By virtue of stochastic analysis methods, we investigate the asymptotics of the mean exit times and probabilistic...In the present paper we consider the small random perturbations of one-dimensional diffosion processes. By virtue of stochastic analysis methods, we investigate the asymptotics of the mean exit times and probabilistical estimates of the exit times as the perturbations tend to zero.展开更多
We consider the maximum likelihood estimator of the unknown parameter in aclass of nonstationary diffusion processes. We give further a precise estimate for the error of theestimator.
Using time reversal for diffusions and Aroson's estimates, we obtain several results on the compact properties of a conditional diffusion process in a small time interval. In particular, we establish the large dev...Using time reversal for diffusions and Aroson's estimates, we obtain several results on the compact properties of a conditional diffusion process in a small time interval. In particular, we establish the large deviation property for a conditional diffusion process.展开更多
基金supported by National Natural Science Foundation of China(11371321)Zhejiang Provincial Natural Science Foundation of China(Y6100663)the Key Research Base of Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statis-tics of Zhejiang Gongshang University)
文摘Let X(1) = {X(1)(s), s ∈ R+} and X(2) = {X(2)(t), t ∈ R+} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X (1) and X (2) are studied. More gener-ally, let E1, E2?(0,∞) and F ?Rd be Borel sets. A necessary condition and a suffcient condition for P{X(1)(E1)∩X(2)(E2)∩F 6=?}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space (R+× R+× Rd,ρb), whereρb is an unsymmetric metric defined in R+× R+× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.
基金Funded by the National Natural Science Foundation of China (No.50675165)the National Key Technology R&D Program (No.2006BAF02A29)
文摘The segregation of thermal diffusion salt bath chromizing process was analyzed. The experimental chromizing ingredients were prepared by the four groups A, B, C, and D. In order to study the segregation status of this case, the cooling molten salt in the crucible was removed by drilling from the heart core of molten salt. The core of molten salt was analyzed by X-ray fluorescence spectroscopy and XRD. Through the analysis, we can conclude that the Cr element deposited in the bottom was 4.51 times than the top. Chloride added to the molten salt will reduce segregation. Meantime we proposed some measures to overcome the segregation problem.
基金supported by the National Natural Science Foundation of China(61473136,61807016)the Fundamental Research Funds for the Central Universities(JUSRP51322B)+1 种基金the 111 Project(B12018)Jiangsu Innovation Program for Graduates(KYLX15 1170)
文摘This paper is concerned with a control problem of a diffusion process with the help of static mesh sensor networks in a certain region of interest and a team of networked mobile actuators carrying chemical neutralizers.The major contribution of this paper can be divided into three parts:the first is the construction of a cyber-physical system framework based on centroidal Voronoi tessellations(CVTs),the second is the convergence analysis of the actuators location,and the last is a novel proportional integral(PI)control method for actuator motion planning and neutralizing control(e.g.,spraying)of a diffusion process with a moving or static pollution source,which is more effective than a proportional(P)control method.An optimal spraying control cost function is constructed.Then,the minimization problem of the spraying amount is addressed.Moreover,a new CVT algorithm based on the novel PI control method,henceforth called PI-CVT algorithm,is introduced together with the convergence analysis of the actuators location via a PI control law.Finally,a modified simulation platform called diffusion-mobile-actuators-sensors-2-dimension-proportional integral derivative(Diff-MAS2D-PID)is illustrated.In addition,a numerical simulation example for the diffusion process is presented to verify the effectiveness of our proposed controllers.
基金Research supported in part by Tianyuan Fund ofr Mathematics of NSFC (10526021)A Grant from Ministry of Education
文摘Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x(L^κB) 〈∞ is proved.
基金Supported by the National Natural Science Foundation of China(201130486) and a Grant from the Ministry of Education of China
文摘The cone condition for x to be tegular for B under the elliptic diffusionprocess was proved. We also gave a necessary and sufficient condition for 0 to be regular for thornunder the elliptic diffusion process.
基金This work is supported by NSFC (10271008 and 10531070)
文摘The entropy production rate of stationary minimal diffusion processes with smooth coefficients is calculated. As a byproduct, the continuity of paths of the minimal diffusion processes is discussed, and that the point at infinity is absorbing is proved.
基金National Natural Science Foundations of China (No. 11071076,No. 11126124)
文摘The hedging problem for insiders is very important in the financial market.The locally risk minimizing hedging was adopted to solve this problem.Since the market was incomplete,the minimal martingale measure was chosen as the equivalent martingale measure.By the F-S decomposition,the expression of the locally risk minimizing strategy was presented.Finally,the local risk minimization was applied to index tracking and its relationship with tracking error variance (TEV)-minimizing strategy was obtained.
文摘In this paper, we propose a Gasser-Müller type spot volatility estimator (abbreviated as GM type estimator) for diffusion process, which is weighted by integrals, it is different from the kernel spot volatility estimator discussed by Kristensen (2010). Under more general conditions, the asymptotic unbiasedness and the asymptotic normality of the GM type estimator are derived. The simulation results show that the GM type spot volatility estimator has good estimation effect, and its mean square error tends to be less than that of the kernel spot volatility estimator discussed by Kristensen (2010), so it provides a selection method for estimating the spot volatility in high frequency data environment.
基金Project supported by the Pioneer and Leading Goose R&D Program of Zhejiang(2020C01190)the Science and Technology Innovation 2025Major Project of Ningbo(2020Z064)+1 种基金the Zhejiang Province Postdoctoral Science Foundation(ZJ2021080)the Inner Mongolia Major Technology Project(2021ZD0035)。
文摘Grain boundary diffusion process(GBDP)was first proposed for sintered Nd-Fe-B magnets to achieve the high utilization efficiency of heavy rare earth elements.Recent success of fabricating high performance nanocomposite magnets by GBDP indicates that this method also exerts huge applicable potential on hot-deformed Nd-Fe-B magnets.In this review,the development and magnetic property enhancement mechanisms of different diffusion methods proposed on hot-deformed magnets were thoroughly elucidated.Moreover,the improve room for further property enhancement and the accompanying problems of GBDP on hot-deformed magnets are also discussed in this article.
基金the National Key Research and Development Program of China(Nos.2022YFB3505004,2022YFB3503400 and 2022YFB3503401)the National Natural Science Foundation of China(Nos.52071143,52171175,U21A2052,and U1908220)+3 种基金the Key R&D project of Zhejiang Province(Nos.2023C01077 and 2021C01023)the Guangdong Basic and Applied Basic Research Foundation(Nos.2023A1515010431 and 2022A1515011453)the GDAS Project of Science and Technology Development(Nos.2019GDASYL-0103067,2022GDASZH-2022010104,and 2022GDASZH-2022030604-04)the China Postdoctoral Science Foundation funded project(2022M720845).
文摘The rare earth-iron-boron magnets based on high abundance rare earths(REs)show potential for costeffective permanent magnets but their hard magnetic properties have to be greatly improved.The grain boundary diffusion process(GBDP)is known as an effective way to improve the coercivity of Nd-Fe-B magnets,however,the conventional diffusion method faces a challenge for Ce-based magnets since there is no enough continuous GB layer as the diffusion channel.Here,a two-step(Nd-Cu doping followed by Nd-Cu diffusion)GBDP was introduced for hot deformed(Ce,La,Y)-Fe-B magnet,and the excellent magnetic properties ofμ0Hc=0.63 T,μ0Mr=0.68 T,and(BH)max=72.4 kJ/m^(3)were achieved.The Nd-Cu doping helps the formation of RE-rich GB layer,and then it acts as the diffusion channel for increasing the ef-ficiency of the subsequent Nd-Cu diffusion and results in the increased volume fraction of continuously distributed GB phase,whose paramagnetism was verified by 57Fe Mössbauer spectrometry.Those paramagnetic GB phases help to form the discontinuous domain walls,as observed by Lorentz transmission electron microscopy,and break the magnetic exchange coupling of RE2Fe14B grains.It thus contributes to the coercivity enhancement of the hot deformed magnet with two-step diffusion,which is further proved by micromagnetic simulation.This study proposes a potential technique to prepare anisotropic hot deformed(Ce,La,Y)-Fe-B magnet with high cost-performance.
基金The authors would like to thank the referees for helpful comments on an earlier version of the paper.This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11771326,11726627,11831014).
文摘For any N≥2 andα=(α1…,αN+1)∈(0,∞)^N+1,letμa^(N)be the Dirichlet distribution with parameterαon the set△(N):={x^μa∈[0,1]^N:∑1≤i≤N^xi≤1}.The multivariate Dirichlct diffusion is associated with the Dirichlet formεa^(N)(f,f):=∑n=i^N∫△(N)(1-∑1≤i≤N^xi)xn(Эnf)^2(x)μα^(N)(dx)with Domain D(εa^(N))being the closure of C^1(△^(N)).We prove the Nash inequalityμa^(N)(f^2)≤Cεa^(N)(f,f)^p/(p+1)μa^(N)(|f|)^2/(p+1),f∈D(εa^(N)),μa^(N)(f)=0 for some constant C>0 and p=(aN+1-1)++∑i^N=11∨(2ai),where the constant p is sharp when max1≤i≤N ai≤1/2 and aN+1≥1.This Nash inequality also holds for the corresponding Fleming-Viot process.
基金Supported by National Natural Science Foundation of China (Grant No. 10871153)
文摘The goal of this paper is to study large deviations for estimator and score function of some time inhomogeneous diffusion process. Large deviation in the non-steepness case with explicit rate functions is obtained by using parameter-dependent change of measure.
基金The authors would like to thank the referees for providing many helpful comments and suggestions. Research of the second author was supported in part by the National Natural Science Foundation of China (Grant No. 11171024).
文摘We consider the asymptotic property of the diffusion processes with Markovian switching. For a general case, we prove a large deviation principle for empirical measures of switching diffusion processes with small parameters.
基金Ying-Tung Fok Education Foundation and NSFCNSFC and by Anhui Education Commitee..
文摘In this paper,a class of reaction diffusion processes with general reaction rates is studied.A necessary and sufficient condition for the reversibility of this calss of reaction diffusion processes is given,and then the ergodicity of these processes is proved.
基金Supported in part by NSFC(Grant No.11771047)Hu Xiang Gao Ceng Ci Ren Cai Ju Jiao Gong Cheng-Chuang Xin Ren Cai(Grant No.2019RS1057)。
文摘In this paper,we define the generalized diffusion operator L=d/dMd/dS for two suitable measures on the line,which includes the generators of the birth-death processes,the one-dimensional diffusion and the gap diffusion among others.Via the standard resolvent approach,the associated generalized diffusion processes are constructed.
基金Supported by the National Natural Science Foundationof China(No.79970 12 0 )
文摘Two typical ARCH models: the ASDARCH model and the APARCH model are analyzed. Let Y k and σ 2 k denote the log returns and the volatility. When the time interval h goes to zero, (Y k,σ 2 k), as a discrete time Markov chain system, weakly converges to a continuous time diffusion process. The continuous time approximation of the ASDARCH model is done using two different methods. With some transformation, these two results are equivalent to high frequency data. The continuous time approximation of the APARCH model is obtained by a different procedure.
基金Research supported in part by NNSFC (19631060) Beijing Nornaal University
文摘Let τ_D denote the lifetime of a diffusion process on domain DR^d. This paper presents a sufficient condition for the exponential moment of τ_D to be finite. Here, both of the domain and the diffusion operator are general. As an application, the main result of Gao(1995) for conditioned diffusions is improved on.
基金the Young Teachers Foundation of Beijing Institute of Technology
文摘In the present paper we consider the small random perturbations of one-dimensional diffosion processes. By virtue of stochastic analysis methods, we investigate the asymptotics of the mean exit times and probabilistical estimates of the exit times as the perturbations tend to zero.
基金Research partially supported by N.S.F.Grants DMS-0203823Doctoral Program Foundation of the Ministry of Education of China,Grant No.20020269015
文摘We consider the maximum likelihood estimator of the unknown parameter in aclass of nonstationary diffusion processes. We give further a precise estimate for the error of theestimator.
文摘Using time reversal for diffusions and Aroson's estimates, we obtain several results on the compact properties of a conditional diffusion process in a small time interval. In particular, we establish the large deviation property for a conditional diffusion process.