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Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
Martin Hutzenthaler, Arnulf Jentzen, Peter E. Kloeden
On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally on…
Taylor expansions of solutions of stochastic partial differential equations with additive noise
Arnulf Jentzen, Peter Kloeden
The solution of a parabolic stochastic partial differential equation (SPDE) driven by an infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does i…
A mild Ito formula for SPDEs
Giuseppe Da Prato, Arnulf Jentzen, Michael Roeckner
This article introduces a certain class of stochastic processes, which we suggest to call mild Ito processes, and a new - somehow mild - Ito type formula for such processes. Exampl…
Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise
Arnulf Jentzen, Michael Roeckner
In this article spatial and temporal regularity of the solution process of a stochastic partial differential equation (SPDE) of evolutionary type with nonlinear multiplicative trac…
A Milstein scheme for SPDEs
Arnulf Jentzen, Michael Roeckner
This article studies an infinite dimensional analog of Milstein's scheme for finite dimensional stochastic ordinary differential equations (SODEs). The Milstein scheme is known to…