Stochastic Taylor Expansions for Functionals of Diffusion Processes

Abstract

In the present paper, a stochastic Taylor expansion of some functional applied to the solution process of an Itô or Stratonovich stochastic differential equation with a multi-dimensional driving Wiener process is given. Therefore, the multi-colored rooted tree analysis is applied in order to obtain a transparent representation of the expansion which is similar to the B-series expansion for solutions of ordinary differential equations in the deterministic setting. Further, some estimates for the mean--square and the mean truncation errors are given.

References in corpus (2)

• Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
• Stochastic Taylor expansions for the expectation of functionals of diffusion processes

Cited by in corpus (4)

• Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds
• A micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations
• High order numerical integrators for single integrand Stratonovich SDEs
• Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations