Impulse Control Problem of Partially Observed Diffusion Processes

The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the only viscosity solution of the corresponding quasi-variational inequality. The authors show the optimal cost function for the problem with incomplete information can be approximated by a sequence of value functions of the previous type.

Large Deviation Theorem for Empirical Measures of Degenerate Diffusion Processes

A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differential equation dX ε(t)=σ(X ε(t)) d W(t)+B(X ε(t)) d t+ εσ～(X ε(t)) d W(t),ε>0. X ε(t) are small random perturbations of the degenerate diffusion process X(t), which satisfies the stochastic differential equation dX(t)=σ(X(t)) d W(t)+B(X(t)) d t. A large deviation theorem for projection measures ν on R r-n (n<r) of empirical measures μ are proved

ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

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.

ENTROPY PRODUCTION RATE OF THE MINIMAL 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 at infinity is absorbing is proved.

Segregation of Molten Salt on Chromizing in Thermal Diffusion Process

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.

An Improved Cooperative Team Spraying Control of a Diffusion Process With a Moving or Static Pollution Source

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.

AN ESTIMATE ON THE DISTRIBUTION AND MOMENTS OF THE LAST EXIT TIME OF AN ELLIPTIC DIFFUSION PROCESS

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.

Criteria for Regularity of Elliptic Diffusion Processes and It’s Application

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.

Cooperative Sensing and Distributed Control of a Diffusion Process Using Centroidal Voronoi Tessellations

This paper considers how to use a group of robots to sense and control a diffusion process.The diffusion process is modeled by a partial differential equation (PDE),which is a both spatially and temporally variant system.The robots can serve as mobile sensors,actuators,or both.Centroidal Voronoi Tessellations based coverage control algorithm is proposed for the cooperative sensing task.For the diffusion control problem,this paper considers spraying control via a group of networked mobile robots equipped with chemical neutralizers,known as smart mobile sprayers or actuators,in a domain of interest having static mesh sensor network for concentration sensing.This paper also introduces the information sharing and consensus strategy when using centroidal Voronoi tessellations algorithm to control a diffusion process.The information is shared not only on where to spray but also on how much to spray among the mobile actuators.Benefits from using CVT and information consensus seeking for sensing and control of a diffusion process are demonstrated in simulation results.

Insiders' Hedging for Jump Diffusion Processes with Applications to Index Tracking

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.

The First- Passage Time Moment of the GNP Diffusion Process to a Determined Value

This paper describes an accurate method of approximating the moments of the first-passage time for the birth and death Gross National Product GNP diffusion process when the GNP is a determined value or constant absorbing barrier. This was done by approximating the differential equations by equivalent difference equations.

The Estimation of the Spot Volatility for Diffusion Process

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.

Cultural materialism behind global cultural diffusion process

In this paper, the author intends to illustrate cultural materialism behind cultural diffusion process. The author first argues that despite the two opposing paradigms of cultural views （differentialism vs. universalism） what is really happening and winning is the third paradigm of mixing cultural perspective as presented in Jan Nederveen Pieterse＇s book Globalization and culture-global Mdlange. Then the author takes Marvin Harris＇ cultural materialism theory as the basis and gives specific evidence from China to illustrate the formation and eventual spread of any ＂new cultural scripts＂, which is done through the transformation process from territorial culture to translocal culture with economic motive behind as the driving force. These Chinese cases of global mixing, in turn, form a further support to Marvin Harris＇s cultural materialism theory.

Recent progress of grain boundary diffusion process for hot-deformed Nd-Fe-B magnets

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.

Grain boundary construction and properties enhancement for hot deformed(Ce,La,Y)-Fe-B magnet by a two-step diffusion process

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.

The joint Laplace transforms for killed diffusion occupation times

The approach of Li and Zhou(2014)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion process up to an independent exponential time e_(q)for 0<a<b.The results are expressed in terms of solutions to the differential equations associated with the diffusion generator.Applying these results,we obtain explicit expressions on the Laplace transform of occupation time and joint occupation time for Brownian motion with drift.

Nash inequality for diffusion processes associated with Dirichlet distributions

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.

Large Deviations for Parameter Estimators of Some Time Inhomogeneous Diffusion Process

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.

Large deviations for empirical measures of switching diffusion processes with small parameters

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.

Ergodicity of Reversible Reaction Diffusion Processes with General Reaction Rates

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.