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ON GENERALIZED FEYNMAN-KAC TRANSFORMATION FOR MARKOV PROCESSES ASSOCIATED WITH SEMI-DIRICHLET FORMS
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作者 韩新方 马丽 《Acta Mathematica Scientia》 SCIE CSCD 2016年第6期1683-1698,共16页
Suppose that X is a right process which is associated with a semi-Dirichlet form (ε, D(ε)) on L2(E; m). Let J be the jumping measure of (ε, D(ε)) satisfying J(E x E- d) 〈 ∞. Let u E D(ε)b := D(... Suppose that X is a right process which is associated with a semi-Dirichlet form (ε, D(ε)) on L2(E; m). Let J be the jumping measure of (ε, D(ε)) satisfying J(E x E- d) 〈 ∞. Let u E D(ε)b := D(ε) N L(E; m), we have the following Pukushima's decomposition u(Xt)-u(X0) --- Mut + Nut. Define Pu f(x) = Ex[eNT f(Xt)]. Let Qu(f,g) = ε(f,g)+ε(u, fg) for f, g E D(ε)b. In the first part, under some assumptions we show that (Qu, D(ε)b) is lower semi-bounded if and only if there exists a constant a0 〉 0 such that /Put/2 ≤eaot for every t 〉 0. If one of these assertions holds, then (Put〉0is strongly continuous on L2(E;m). If X is equipped with a differential structure, then under some other assumptions, these conclusions remain valid without assuming J(E x E - d) 〈 ∞. Some examples are also given in this part. Let At be a local continuous additive functional with zero quadratic variation. In the second part, we get the representation of At and give two sufficient conditions for PAf(x) = Ex[eAtf(Xt)] to be strongly continuous. 展开更多
关键词 semi-Dirichlet form generalized Feynman-Kac semigroup strong continuity lower semi-bounded representation of local continuous additive functionalwith zero quadratic variation
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THE EXISTENCE AND UNIQUENESS OF THE DECAYING POSITIVE ENTIRE SOLUTIONS FOR A CLASS OF SEMILIN EARELLIPTIC EQUATIONS
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作者 田根宝 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第8期765-777,共13页
This paper first proves the following equations△u-m ̄2u+f(x,u)=0, x(R ̄n,n≥3 m>0 existence of decaying positive entire solution, then emphatically, proves this solution'suniqueness.
关键词 weak supersolution weak subsolution monotone convergencetheorem . nonincreasing. nondecreasing locally Hldercontinuous.locally Lipschitz continuous strong maximumprinciple
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Uniqueness of Viscosity Solutions to the Dirichlet Problem Involving Infinity Laplacian
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作者 Hong Sun Fang Liu 《Advances in Pure Mathematics》 2023年第10期662-673,共12页
In this paper, we study the Dirichlet boundary value problem involving the highly degenerate and h-homogeneous quasilinear operator associated with the infinity Laplacian, where the right hand side term is and the bou... In this paper, we study the Dirichlet boundary value problem involving the highly degenerate and h-homogeneous quasilinear operator associated with the infinity Laplacian, where the right hand side term is and the boundary value is . First, we establish the comparison principle by the double variables method based on the viscosity solutions theory for the general equation in. We propose two different conditions for the right hand side and get the comparison principle results under different conditions by making different perturbations. Then, we obtain the uniqueness of the viscosity solution to the Dirichlet boundary value problem by the comparison principle. Moreover, we establish the local Lipschitz continuity of the viscosity solution. 展开更多
关键词 Infinity Laplacian Comparison Principle UNIQUENESS Local Lipschitz Continuity
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THE HOLDER CONTINUITY OF GENERALIZED SOLUTIONS OF A CLASS QUASILINEAR PARABOLIC EQUATIONS
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作者 王向东 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第6期573-583,共11页
Let A and B satisfy the structural conditions (2), the local Holder continuity interior to Q = G X (0, T) is proved for the generalized solutions of quasilinear parabolic equations as follows: u(t) - divA(x, t, u, del... Let A and B satisfy the structural conditions (2), the local Holder continuity interior to Q = G X (0, T) is proved for the generalized solutions of quasilinear parabolic equations as follows: u(t) - divA(x, t, u, del u) + B(x, t, U, del u) = 0. 展开更多
关键词 parabolic equation natural growth condition generalized solution local Holder continuity
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AN EFFICIENT ADER DISCONTINUOUS GALERKIN SCHEME FOR DIRECTLY SOLVING HAMILTON-JACOBI EQUATION 被引量:1
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作者 Junming Duan Huazhong Tang 《Journal of Computational Mathematics》 SCIE CSCD 2020年第1期58-83,共26页
This paper proposes an efficient ADER(Arbitrary DERivatives in space and time)discontinuous Galerkin(DG)scheme to directly solve the Hamilton-Jacobi equation.Unlike multi-stage Runge-Kutta methods used in the Runge-Ku... This paper proposes an efficient ADER(Arbitrary DERivatives in space and time)discontinuous Galerkin(DG)scheme to directly solve the Hamilton-Jacobi equation.Unlike multi-stage Runge-Kutta methods used in the Runge-Kutta DG(RKDG)schemes,the ADER scheme is one-stage in time discretization,which is desirable in many applications.The ADER scheme used here relies on a local continuous spacetime Galerkin predictor instead of the usual Cauchy-Kovalewski procedure to achieve high order accuracy both in space and time.In such predictor step,a local Cauchy problem in each cell is solved based on a weak formulation of the original equations in spacetime.The resulting spacetime representation of the numerical solution provides the temporal accuracy that matches the spatial accuracy of the underlying DG solution.The scheme is formulated in the modal space and the volume integral and the numerical fluxes at the cell interfaces can be explicitly written.The explicit formulae of the scheme at third order is provided on two-dimensional structured meshes.The computational complexity of the ADER-DG scheme is compared to that of the RKDG scheme.Numerical experiments are also provided to demonstrate the accuracy and efficiency of our scheme. 展开更多
关键词 Hamilton-Jacobi equation ADER Discontinuous Galerkin methods Local continuous spacetime Galerkin predictor High order accuracy
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Local Continuity Modulus for Wiener and Infinite Dimensional OU Processes 被引量:3
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作者 Lu Chuanrong Shen Siwei Wang Xiuyun Department of Mathematics Hangzhou University Hangzhou, 310028 China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1994年第2期219-224,共6页
In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W(s)|/(2s log log(1/s))<sup>1/2</sup>=1 a.s. This result was given by Csrg... In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W(s)|/(2s log log(1/s))<sup>1/2</sup>=1 a.s. This result was given by Csrg and Revesz (1981), but the proof gets them nowhere. We also gave a similar local continuity modulus result for the infinite dimensional OU processes. 展开更多
关键词 In OU Local Continuity Modulus for Wiener and Infinite Dimensional OU Processes
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A New Family of High Order Unstructured MOOD and ADER Finite Volume Schemes for Multidimensional Systems of Hyperbolic Conservation Laws 被引量:1
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作者 Raphael Loubere Michael Dumbser Steven Diot 《Communications in Computational Physics》 SCIE 2014年第8期718-763,共46页
In this paper,we investigate the coupling of the Multi-dimensional Optimal Order Detection(MOOD)method and the Arbitrary high order DERivatives(ADER)approach in order to design a new high order accurate,robust and com... In this paper,we investigate the coupling of the Multi-dimensional Optimal Order Detection(MOOD)method and the Arbitrary high order DERivatives(ADER)approach in order to design a new high order accurate,robust and computationally efficient Finite Volume(FV)scheme dedicated to solve nonlinear systems of hyperbolic conservation laws on unstructured triangular and tetrahedral meshes in two and three space dimensions,respectively.The Multi-dimensional Optimal Order Detection(MOOD)method for 2D and 3D geometries has been introduced in a recent series of papers for mixed unstructured meshes.It is an arbitrary high-order accurate Finite Volume scheme in space,using polynomial reconstructions with a posteriori detection and polynomial degree decrementing processes to deal with shock waves and other discontinuities.In the following work,the time discretization is performed with an elegant and efficient one-step ADER procedure.Doing so,we retain the good properties of the MOOD scheme,that is to say the optimal high-order of accuracy is reached on smooth solutions,while spurious oscillations near singularities are prevented.The ADER technique permits not only to reduce the cost of the overall scheme as shown on a set of numerical tests in 2D and 3D,but it also increases the stability of the overall scheme.A systematic comparison between classical unstructured ADER-WENO schemes and the new ADER-MOOD approach has been carried out for high-order schemes in space and time in terms of cost,robustness,accuracy and efficiency.The main finding of this paper is that the combination of ADER with MOOD generally outperforms the one of ADER and WENO either because at given accuracy MOOD is less expensive(memory and/or CPU time),or because it is more accurate for a given grid resolution.A large suite of classical numerical test problems has been solved on unstructured meshes for three challenging multi-dimensional systems of conservation laws:the Euler equations of compressible gas dynamics,the classical equations of ideal magneto-Hydrodynamics(MHD)and finally the relativistic MHD equations(RMHD),which constitutes a particularly challenging nonlinear system of hyperbolic partial differential equation.All tests are run on genuinely unstructured grids composed of simplex elements. 展开更多
关键词 Finite Volume high-order conservation law polynomial reconstruction ADER MOOD hyperbolic PDE unstructured meshes finite volume one-step time discretization local continuous space-time Galerkin method WENO Euler equations MHD equations relativistic MHD equations.
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Semibounded Nonlinear Evolution Equations with Application to the KdV Equations
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作者 Xiao-Ling Xiang, Chun-Xia Fan, Wei WeiDepartment of Mathematics, Guizhou University, Guiyang 550025, China 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2003年第2期267-280,共14页
Abstract Existence of solutions for semibounded nonlinear evolution equations is established. This gives more accurate estimate of solutions and conditions of existence are more easily validated. Our results are succe... Abstract Existence of solutions for semibounded nonlinear evolution equations is established. This gives more accurate estimate of solutions and conditions of existence are more easily validated. Our results are successfully applied to prove existence and uniqueness of solutions for some KdV type equations. 展开更多
关键词 Keywords Semiboundedness admissible triplet Galerkin equation local Lipschitz continuity existence UNIQUENESS KdV equation.
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ON LOCAL CONTINUITY MODULI FOR GAUSSIAN PROCESSES
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作者 陆传荣 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1996年第1期93-100,共8页
In this paper, we get three local continuity moduli theorems for the almost surely continuous, stationary increments Gaussian process {Y(t), t0}, the partial sum processes X(t,N)= (t) of infinite dimensional Ornstein-... In this paper, we get three local continuity moduli theorems for the almost surely continuous, stationary increments Gaussian process {Y(t), t0}, the partial sum processes X(t,N)= (t) of infinite dimensional Ornstein-Uhlenbeck processes {Xk(t), t0}, and lp-valued Gaussian processes {Y(t), t0}={Xk(t), t0}, separately. The first theorem implies the local continuity modulus theorem for the series X(t)=, Xk(t) of infinite dimensional OrnsteinUhlenbeck processes which has been obtained in [3]. 展开更多
关键词 Gaussian process infinite dimensional Ornstein-Uhlenbeck process local continuity modulus
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Singularities of the Radon Transform of a Class of Piecewise Smooth Functions in R^2
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作者 Gang-tong Qu 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2011年第2期191-208,共18页
A class of piecewise smooth functions in R2 is considered. The propagation law of the Radon transform of the function is derived. The singularities inversion formula of the Radon transform is derived from the propagat... A class of piecewise smooth functions in R2 is considered. The propagation law of the Radon transform of the function is derived. The singularities inversion formula of the Radon transform is derived from the propagation law. The examples of singularities and singularities inversion of the Radon transform are given. 展开更多
关键词 singularities of the Radon transform local Lipschitz continuous singularities inversion
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BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH RANDOM MEASURES 被引量:1
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作者 夏建明 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2000年第3期225-234,共10页
Backward stochastic differential equations (BSDE) are discussed in many papers. However, in those papers, only Brownian motion and Poisson process are considered. In this paper, we consider BSDE driven by continuous l... Backward stochastic differential equations (BSDE) are discussed in many papers. However, in those papers, only Brownian motion and Poisson process are considered. In this paper, we consider BSDE driven by continuous local martingales and random measures. 展开更多
关键词 Backward stochastic differential equations continuous local martingale random measures
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