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An exponential Wagner-Platen type scheme for SPDEs
Sebastian Becker, Arnulf Jentzen, Peter E. Kloeden
The strong numerical approximation of semilinear stochastic partial differential equations (SPDEs) driven by infinite dimensional Wiener processes is investigated. There are a numb…
Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations
Martin Hutzenthaler, Arnulf Jentzen, Xiaojie Wang
Exponential integrability properties of numerical approximations are a key tool for establishing positive rates of strong and numerically weak convergence for a large class of nonl…
Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations
Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen
Recently, Hairer et. al (2012) showed that there exist SDEs with infinitely often differentiable and globally bounded coefficient functions whose solutions fail to be locally Lipsc…
Galerkin approximations for the stochastic Burgers equation
Dirk Blömker, Arnulf Jentzen
Existence and uniqueness for semilinear stochastic evolution equations with additive noise by means of finite dimensional Galerkin approximations is established and the convergence…
Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations
E. Weinan, Arnulf Jentzen, Hao Shen
This article analyzes well-definedness and regularity of renormalized powers of Ornstein-Uhlenbeck processes and uses this analysis to establish local existence, uniqueness and reg…