scholarly journals Weak Convergence Rates for Euler-Type Approximations of Semilinear Stochastic Evolution Equations with Nonlinear Diffusion Coefficients

2020 ◽  
Author(s):  
Arnulf Jentzen ◽  
Ryan Kurniawan
Keyword(s):  
Weak Convergence ◽  
Diffusion Coefficients ◽  
Nonlinear Diffusion ◽  
Evolution Equations ◽  
Convergence Rates ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

scholarly journals Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities

2019 ◽  
Vol 40 (2) ◽  
pp. 1005-1050 ◽  
Author(s):  
Arnulf Jentzen ◽  
Primož Pušnik
Keyword(s):  
Strong Convergence ◽  
Approximation Method ◽  
Evolution Equations ◽  
Convergence Rates ◽  
Reaction Diffusion ◽  
Convergence Result ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Lipschitz Continuous ◽  
Strong Convergence Rates

Abstract In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. We establish strong convergence rates for this approximation method in the case of semilinear stochastic evolution equations with globally monotone coefficients. Our strong convergence result, in particular, applies to a class of stochastic reaction–diffusion partial differential equations.

scholarly journals Smoothness of solutions of stochastic evolution equations and the existence of a filtering transition density

1981 ◽  
Vol 84 ◽  
pp. 195-208 ◽  
Author(s):  
B. L. Rozovskii ◽  
A. Shimizu
Keyword(s):  
Evolution Equations ◽  
Transition Density ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Smoothness Of Solutions

In this paper, we shall discuss the smoothness of solutions of stochastic evolution equations, which has been investigated in N. V. Krylov and B. L. Rozovskii [2] [3], to establish the existence of a filtering transition density.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

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