A sample path large deviation principle for \(L^2\)-martingale measure processes
type: Item
instance of: scholarly article
title: A sample path large deviation principle for \(L^2\)-martingale measure processes
zbMATH Open document ID: 0951.60024
DOI: 10.1016/S0007-4497(99)00107-4
author: Boualem Djehiche
author: Ingemar Kaj
published in: Bulletin des Sciences Mathématiques
publication date: 2000-02-01T00:00:00Z
review text: Subject of this paper is a class of infinite-dimensional diffusions that allow for descriptions via martingale problems involving \(L^2\)-martingale measures. The processes under consideration include the Fleming-Viot process, \({\mathcal S}^\prime(R^d)\)-valued cylindrical Brownian motion, super-Brownian motion, and a super-Brownian motion in a random environment introduced by \textit{L. Mytnik} [Ann. Probab. 24, No. 4, 1953-1978 (1996; Zbl 0874.60041)]. The main result of the paper is a sample path large deviation principle of Freidlin-Wentzell type, to which a Hamiltonian approach is taken. The occurring rate function is studied in some detail: Several equivalent representations are given, the regularity of paths with finite rate is studied, and these paths are related to a certain McKean-Vlasov equation. In the general formulation of the large deviation principle, upper and lower bounds are asymmetric in the sense that, for the lower bound, only those paths are taken into account which are sufficiently regular solutions to the McKean-Vlasov equation. In the ''non-interacting'' case of Gaussian white noise, a large deviation principle in the ordinary sense is obtained.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 1385248
zbMATH Keywords: Freidlin-Wentzell large deviations
zbMATH Keywords: measure-valued processes
zbMATH Keywords: martingale measure
reviewed by: Alexander Schied
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1385248