Talagrand’s quadratic transportation cost inequalities for SPDEs driven by fractional noises with two reflection walls

Differential Equations ◽

Transportation Cost ◽

Uniform Norm ◽

Continuous Functions ◽

Partial Differential ◽

Girsanov’S Transformation ◽

Using the method of Girsanov’s transformation, we investigate Talagrand’s quadratic transportation cost inequalities for the laws of the solutions of stochastic partial differential equations (SPDEs) with two reflection walls under the uniform norm on the continuous functions space. These equations are driven by fractional noises.

Stochastic partial differential equations driven by space-time fractional noises

Stochastics and Dynamics ◽

10.1142/s0219493719500126 ◽

2019 ◽

Vol 19 (02) ◽

pp. 1950012

Author(s):

Ying Hu ◽

Yiming Jiang ◽

Zhongmin Qian

Keyword(s):

Differential Equations ◽

Space Time ◽

Partial Differential ◽

The Family ◽

Non Local ◽

In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying at first the non-local SPDEs and thereafter showing the convergence of the family of these equations. The limit gives the solution of the SPDE.

Stochastic partial differential equations with gradient driven by space-time fractional noises

Frontiers of Mathematics in China ◽

10.1007/s11464-021-0875-z ◽

2021 ◽

Author(s):

Yiming Jiang ◽

Xu Yang

Keyword(s):

Differential Equations ◽

Space Time ◽

Partial Differential ◽

Asymptotic analysis of a kernel estimator for parabolic stochastic partial differential equations driven by fractional noises

Frontiers of Mathematics in China ◽

10.1007/s11464-017-0665-9 ◽

2017 ◽

Vol 13 (1) ◽

pp. 187-201

Author(s):

Suxin Wang ◽

Yiming Jiang

Keyword(s):

Differential Equations ◽

Asymptotic Analysis ◽

Kernel Estimator ◽

Partial Differential ◽

Discrete sample estimation for gaussian random fields generated by stochastic partial differential equations

Communication in Statistics- Theory and Methods ◽

10.1080/03610929808828954 ◽

1998 ◽

Vol 14 (4) ◽

pp. 883-903

Author(s):

Jaroslav Mohapl

Keyword(s):

Differential Equations ◽

Random Fields ◽

Gaussian Random Fields ◽

Partial Differential ◽

Discrete Sample

Fitting Stochastic Partial Differential Equations to Spatial Data

10.21236/ada279870 ◽

1993 ◽

Author(s):

Richard H. Jones

Keyword(s):

Differential Equations ◽

Spatial Data ◽

Partial Differential

Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

Stochastic Partial Differential Equations Analysis and Computations ◽

10.1007/s40072-021-00199-6 ◽

2021 ◽

Author(s):

Shohei Nakajima

Keyword(s):

Differential Equations ◽

Weak Solutions ◽

Fractional Laplacian ◽

Existence Of Solutions ◽

Partial Differential ◽

Continuity Theorem ◽

Existence Of Weak Solutions ◽

One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.