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
In this paper,we prove a Talagrand’s T2 transportation cost-information inequality for the law of the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise,which is white in time and which has...In this paper,we prove a Talagrand’s T2 transportation cost-information inequality for the law of the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise,which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H∈(1/4,1/2)in the space variable,on the continuous path space with respect to the weighted L2-norm.展开更多
We prove some transportation inequalities for hidden Markov chains, generalize the results proved by Kontorovich and Ramanan in two directions and give some applications to log-likelihood functions and hypothesis test...We prove some transportation inequalities for hidden Markov chains, generalize the results proved by Kontorovich and Ramanan in two directions and give some applications to log-likelihood functions and hypothesis testing.展开更多
In this paper,we prove Talagrand’s T2 transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise,which is fractional for a time variable with the Hurst index H∈(1/2,1...In this paper,we prove Talagrand’s T2 transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise,which is fractional for a time variable with the Hurst index H∈(1/2,1),and is correlated for the spatial variable.The Girsanov theorem for fractional-colored Gaussian noise plays an important role in the proof.展开更多
This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation techn...This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...展开更多
Using the method of Girsanov transformation, we establish the Talagrand’s T 2-inequality for diffusion on the path space C([0,N],? d ) with respect to a uniform metric, with the constant independent of N. This improv...Using the method of Girsanov transformation, we establish the Talagrand’s T 2-inequality for diffusion on the path space C([0,N],? d ) with respect to a uniform metric, with the constant independent of N. This improves the known results for the L 2-metric.展开更多
We establish Talagrand＇s T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type＇s approximations and the known results in the finite dimensional ca...We establish Talagrand＇s T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type＇s approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction- Diffusion equations are provided.展开更多
In this paper, we study some functional inequalities （such as Poincar@ inequality, loga- rithmic Sobolev inequality, generalized Cheeger isoperimetric inequality, transportation-information inequality and transportat...In this paper, we study some functional inequalities （such as Poincar@ inequality, loga- rithmic Sobolev inequality, generalized Cheeger isoperimetric inequality, transportation-information inequality and transportation-entropy inequality） for reversible nearest-neighbor Markov processes on connected finite graphs by means of （random） path method. We provide estimates of the involved constants.展开更多
By using the dimension-free Harnack inequality, the coupling method, and Bakry-Emery＇s argument, some explicit lower bounds are presented for the constant of the Beckner type inequality on compact manifolds. As appli...By using the dimension-free Harnack inequality, the coupling method, and Bakry-Emery＇s argument, some explicit lower bounds are presented for the constant of the Beckner type inequality on compact manifolds. As applications, the Beckner inequality and the transportation cost inequality are established for a class of continuous spin systems. In particular, some results in [1, 2] are generalized.展开更多
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.
基金Supported by Shanghai Sailing Program(Grant No.21YF1415300)。
文摘In this paper,we prove a Talagrand’s T2 transportation cost-information inequality for the law of the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise,which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H∈(1/4,1/2)in the space variable,on the continuous path space with respect to the weighted L2-norm.
基金supported by the Youth Innovation Foundation of Zhongnan University of Economics and Law from the Fundamental Research Funds for the Central Universities of China (Grant No. 2009004/31540911202)
文摘We prove some transportation inequalities for hidden Markov chains, generalize the results proved by Kontorovich and Ramanan in two directions and give some applications to log-likelihood functions and hypothesis testing.
基金supported by the Shanghai Sailing Program (21YF1415300)the Natural Science Foundation of China (12101392)supported by the Natural Science Foundation of China (11871382,11771161).
文摘In this paper,we prove Talagrand’s T2 transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise,which is fractional for a time variable with the Hurst index H∈(1/2,1),and is correlated for the spatial variable.The Girsanov theorem for fractional-colored Gaussian noise plays an important role in the proof.
基金supported by the NSF China#10571075NSF-Guangdong China#04010473+1 种基金The research of the second author was supported by Jinan University Foundation#51204033the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State education Ministry#2005-383
文摘This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...
文摘Using the method of Girsanov transformation, we establish the Talagrand’s T 2-inequality for diffusion on the path space C([0,N],? d ) with respect to a uniform metric, with the constant independent of N. This improves the known results for the L 2-metric.
基金Project supported by the Yangtze Scholarship Program
文摘We establish Talagrand＇s T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type＇s approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction- Diffusion equations are provided.
基金Supported by NSFC(Grant Nos.11371283,11571043,11301498 and 11431014)985 Pro jects and the Fundamental Research Funds for the Central Universities
文摘In this paper, we study some functional inequalities （such as Poincar@ inequality, loga- rithmic Sobolev inequality, generalized Cheeger isoperimetric inequality, transportation-information inequality and transportation-entropy inequality） for reversible nearest-neighbor Markov processes on connected finite graphs by means of （random） path method. We provide estimates of the involved constants.
基金Project supported by the National Natural Scienoe Fbundation of China (No.10121101)the Research Fund for the Doctoral Program of Higher Education (No.20040027009).
文摘By using the dimension-free Harnack inequality, the coupling method, and Bakry-Emery＇s argument, some explicit lower bounds are presented for the constant of the Beckner type inequality on compact manifolds. As applications, the Beckner inequality and the transportation cost inequality are established for a class of continuous spin systems. In particular, some results in [1, 2] are generalized.
