New representations of the Taylor-Stratonovich expansion
type: Item
instance of: scholarly article
title: New representations of the Taylor-Stratonovich expansion
zbMATH Open document ID: 1075.60057
DOI: 10.1023/A:1026138522239
author: D. F. Kuznetsov
published in: Journal of Mathematical Sciences (New York)
publication date: 2005-06-23T00:00:00Z
review text: Consider a regular functional \(R(x_s, s)\) of some \(\mathbb{R}^d\)-valued diffusion process \((x_s)\) which solves some well-behaved stochastic differential equation. A new variant of the Taylor expansion of \(R(x_s,s)\) near \(s= t\) is given, in terms of the multiple Stratonovich integrals \[ \int^s_t(t- \tau_1)^{l_k}\cdots \int^{\tau_{k-1}}_t (t- \tau_k)^{l_1}\circ dw^{i_1}_{\tau_k}\circ\cdots\circ dw^{i_k}_{\tau_1}, \] or alternatively \[ \int^s_t(s- \tau_1)^{l_k}\cdots \int^{\tau_{k-1}}_t (s- \tau_k)^{l_1}\circ dw^{i_1}_{\tau_k}\circ\cdots\circ dw^{i_k}_{\tau_1}. \] These formulas are intended to be useful for numerical solving of Itô stochastic differential equations.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 2182729
zbMATH Keywords: Itô integral
zbMATH Keywords: mulitple Stratonovich integral
zbMATH Keywords: Taylor expansion
zbMATH Keywords: diffusion process
zbMATH Keywords: stochastic differential equation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2182729