We discuss stochastic functional partial differential equations and neutral partial differential equations of retarded type driven by fractional Brownian motion with Hurst parameter H 〉 1/2. Using the Girsanov transf...We discuss stochastic functional partial differential equations and neutral partial differential equations of retarded type driven by fractional Brownian motion with Hurst parameter H 〉 1/2. Using the Girsanov transformation argument, we establish the quadratic transportation inequalities for the law of the mild solution of those equations driven by fractional Brownian motion under the L2 metric and the uniform metric.展开更多
Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling use...Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling used by F. -Y. Wang [Ann. Probab., 2012, 42（3）： 994-1019]. Log-Harnack inequality is established for a class of stochastic evolution equations with non- Lipschitz coefficients which includes hyperdissipative Navier-Stokes/Burgers equations as examples. The integration by parts formula is extended to the path space of stochastic functional partial differential equations, then a Dirichlet form is defined and the log-Sobolev inequality is established.展开更多
In this paper,we study a discontinuous Galerkin numerical scheme for a class of elliptic stochastic partial differential equations (abbr.elliptic SPDEs) driven by space white noises with homogeneous Dirichlet boundary...In this paper,we study a discontinuous Galerkin numerical scheme for a class of elliptic stochastic partial differential equations (abbr.elliptic SPDEs) driven by space white noises with homogeneous Dirichlet boundary conditions for two and three space dimensions.We also establish L2 error estimates for the scheme.In particular,a numerical test for d = 2 is presented at the end of the article.展开更多
基金Supported by the National Natural Science Foundation of China(70671074)the Research Foundation of Tianjin University of Science and Technology(20080207)
基金supported by the Key Laboratory of Random Complex Structures and Data Scienc, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 973 Project (2006CB8059000)Science Fund for Creative Research Groups (10721101)+1 种基金the National Science Foundation of China (10671197)the Science Foundation of Jiangsu Province (BK2006032, 06-A-038, 07-333)
文摘This paper discusses the ergodicity of a linear stochastic partial differential equation drivenby Lvy noise.
基金Acknowledgements The authors would like to thank the referees for helpful suggestions which allowed them to improve the presentation of this paper. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11271093） and the Science Research Project of Hubei Provincial Department Of Education （No. Q20141306）.
文摘We discuss stochastic functional partial differential equations and neutral partial differential equations of retarded type driven by fractional Brownian motion with Hurst parameter H 〉 1/2. Using the Girsanov transformation argument, we establish the quadratic transportation inequalities for the law of the mild solution of those equations driven by fractional Brownian motion under the L2 metric and the uniform metric.
文摘Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling used by F. -Y. Wang [Ann. Probab., 2012, 42（3）： 994-1019]. Log-Harnack inequality is established for a class of stochastic evolution equations with non- Lipschitz coefficients which includes hyperdissipative Navier-Stokes/Burgers equations as examples. The integration by parts formula is extended to the path space of stochastic functional partial differential equations, then a Dirichlet form is defined and the log-Sobolev inequality is established.
文摘In this paper,we study a discontinuous Galerkin numerical scheme for a class of elliptic stochastic partial differential equations (abbr.elliptic SPDEs) driven by space white noises with homogeneous Dirichlet boundary conditions for two and three space dimensions.We also establish L2 error estimates for the scheme.In particular,a numerical test for d = 2 is presented at the end of the article.
