A large deviation principle for small perturbations of random evolution equations in Hoelder norm
type: Item
instance of: scholarly article
title: A large deviation principle for small perturbations of random evolution equations in Hoelder norm
zbMATH Open document ID: 0890.60023
DOI: 10.1016/S0304-4149(97)00020-3
author: D. Massart
published in: Stochastic Processes and their Applications
publication date: 1998-03-29T00:00:00Z
review text: Large deviation estimates of Wentzell-Freidlin type in Hölder norms with exponent \(\alpha <\frac {1}{2}\) for a stochastic differential equation of the form \[ dX^\varepsilon (t)=b(X^\varepsilon (t),Y(t))+\varepsilon ^{1/2}\sigma (X^\varepsilon (t))dW(t), \qquad x^\varepsilon (0)=x, \] are proved where \(W(t)\) is a standard Brownian motion and \(Y(t)\) is a random process independent of \(W\). The coefficients \(b:R^d\times R^m \to R^d\) and \(\sigma :R^d\to M_{d\times d}\) are assumed to be Lipschitz continuous and bounded, the diffusion matrix is uniformly positive definite. For analogous results for diffusion processes cf. \textit{P. Baldi, G. Ben Arous} and \textit{G. Kerkyacharian} [Stochastic Processes Appl. 42, No. 1, 171-180 (1992; Zbl 0757.60014)].
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 1134836
zbMATH Keywords: large deviations
zbMATH Keywords: Hölder norm
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1134836