A function space large deviation principle for certain stochastic integrals
type: Item
instance of: scholarly article
title: A function space large deviation principle for certain stochastic integrals
zbMATH Open document ID: 0682.60018
DOI: 10.1007/BF00333151
publication date: 1989-01-01T00:00:00Z
review text: Let X(t) be a diffusion process on a compact manifold and \[ Y(t)=\int^{t}_{0}Y_ 0(X(s))ds+\sum^{d}_{k=1}\int^{t}_{0}Y_ k(X(s))\circ d\beta_ k(s), \] where \(\beta_ k(\cdot)\), \(1\leq k\leq d\), are independent Wiener processes. The authors prove large deviations principles for \[ \{N^{- 1}\sum^{N-1}_{k=0}(Y(k+t)-Y(k)),\quad 0\leq t\leq 1\}_{N=1,2,3,...}\quad and\quad for\quad \{T^{-1}Y(tT),\quad 0\leq t\leq 1\}_{T\geq 0} \] and identify the corresponding rate functions on C([0,1],\({\mathbb{R}})\). An application to the asymptotics of the Lyapunov exponent of a homogeneous system is given.
reviewed by: Ludwig Arnold
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 4117549
zbMATH Keywords: stochastic integrals
zbMATH Keywords: large deviations principles
zbMATH Keywords: asymptotics of the Lyapunov exponent
author: Jean-Dominique Deuschel
author: Daniel W. Stroock
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4117549