Flots et series de Taylor stochastiques

Research output: Contribution to journalArticle

Abstract

We study the expansion of the solution of a stochastic differential equation as an (infinite) sum of iterated stochastic (Stratonovitch) integrals. This enables us to give a universal and explicit formula for any invariant diffusion on a Lie group in terms of Lie brackets, as well as a universal and explicit formula for the brownian motion on a Riemannian manifold in terms of derivatives of the curvature tensor. The first of these formulae contains, and extends to the non nilpotent case, the results of Doss [6], Sussmann [17], Yamato [18], Fliess and Normand-Cyrot [7], Krener and Lobry [19] and Kunita [11] on the representation of solutions of stochastic differential equations.

Original languageFrench
Pages (from-to)29-77
Number of pages49
JournalProbability Theory and Related Fields
Volume81
Issue number1
DOIs
StatePublished - Feb 1989

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Mathematics(all)

Cite this

Flots et series de Taylor stochastiques. / Arous, Gérard Ben.

In: Probability Theory and Related Fields, Vol. 81, No. 1, 02.1989, p. 29-77.

Research output: Contribution to journalArticle

@article{c1bf4d9cc47f486dab226b71e88bf405,
title = "Flots et series de Taylor stochastiques",
abstract = "We study the expansion of the solution of a stochastic differential equation as an (infinite) sum of iterated stochastic (Stratonovitch) integrals. This enables us to give a universal and explicit formula for any invariant diffusion on a Lie group in terms of Lie brackets, as well as a universal and explicit formula for the brownian motion on a Riemannian manifold in terms of derivatives of the curvature tensor. The first of these formulae contains, and extends to the non nilpotent case, the results of Doss [6], Sussmann [17], Yamato [18], Fliess and Normand-Cyrot [7], Krener and Lobry [19] and Kunita [11] on the representation of solutions of stochastic differential equations.",
author = "Arous, {G{\'e}rard Ben}",
year = "1989",
month = "2",
doi = "10.1007/BF00343737",
language = "French",
volume = "81",
pages = "29--77",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer New York",
number = "1",

}

TY - JOUR

T1 - Flots et series de Taylor stochastiques

AU - Arous, Gérard Ben

PY - 1989/2

Y1 - 1989/2

N2 - We study the expansion of the solution of a stochastic differential equation as an (infinite) sum of iterated stochastic (Stratonovitch) integrals. This enables us to give a universal and explicit formula for any invariant diffusion on a Lie group in terms of Lie brackets, as well as a universal and explicit formula for the brownian motion on a Riemannian manifold in terms of derivatives of the curvature tensor. The first of these formulae contains, and extends to the non nilpotent case, the results of Doss [6], Sussmann [17], Yamato [18], Fliess and Normand-Cyrot [7], Krener and Lobry [19] and Kunita [11] on the representation of solutions of stochastic differential equations.

AB - We study the expansion of the solution of a stochastic differential equation as an (infinite) sum of iterated stochastic (Stratonovitch) integrals. This enables us to give a universal and explicit formula for any invariant diffusion on a Lie group in terms of Lie brackets, as well as a universal and explicit formula for the brownian motion on a Riemannian manifold in terms of derivatives of the curvature tensor. The first of these formulae contains, and extends to the non nilpotent case, the results of Doss [6], Sussmann [17], Yamato [18], Fliess and Normand-Cyrot [7], Krener and Lobry [19] and Kunita [11] on the representation of solutions of stochastic differential equations.

UR - http://www.scopus.com/inward/record.url?scp=0002790129&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002790129&partnerID=8YFLogxK

U2 - 10.1007/BF00343737

DO - 10.1007/BF00343737

M3 - Article

AN - SCOPUS:0002790129

VL - 81

SP - 29

EP - 77

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 1

ER -