On the Onsager-Machlup functional of diffusion processes around non \(C^ 2\) curves
type: Item
instance of: scholarly article
title: On the Onsager-Machlup functional of diffusion processes around non \(C^ 2\) curves
zbMATH Open document ID: 0696.60073
published in: The Annals of Probability
publication date: 1989-01-01T00:00:00Z
review text: For a solution of the stochastic differential equation \(dX_ t=f(X_ t)dt+dW_ t\), where W is the standard n-dimensional Brownian motion, \(f_ i\in C_ b^ 2({\mathbb{R}}^ n)\), \(i=1,2,...,n\), the asymptotic behaviour of \[ P\{\| \phi -x\| <\epsilon \}/P\{\| W\| \leq \epsilon \} \] is computed as \(\epsilon\) \(\to 0\) for \(\phi \in C^{1+\alpha}\), \(\alpha >0\), deterministic on [0,T]. Here \(\| \psi \| =| \max_{u\in [0,T]}| \psi (u)|,\) and \(| \cdot |\) is the Euclidean norm in \(R^ N\).
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 93E14
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 4140964
zbMATH Keywords: stochastic differential equation
author: Ofer Zeitouni
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991255
OpenAlex ID: W2092047309
DOI: 10.1214/AOP/1176991255
description: scientific article; zbMATH DE number 4140964