Stochastic processes on random domains
type: Item
instance of: scholarly article
title: Stochastic processes on random domains
zbMATH Open document ID: 0621.60040
author: E. B. Dynkin
author: Patrick J. Fitzsimmons
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77314
review text: This paper is devoted to study stochastic processes with a random parameter set. The main result is a characterization of the finite dimensional distributions of a stochastic process whose parameter domain is a random open convex subset of \(R^ d\). This result generalizes a previous work of \textit{S. E. Kuznetsov} [Teor. Veroyatn. Primen. 18, 596- 601 (1973; Zbl 0296.60049)], and its proof is based on two theorems: (1) A characterization of the finite-dimensional distributions of a random open convex subset of \(R^ d\), which is a refinement of a theorem of \textit{G. Choquet} [Ann. Inst. Fourier 5, 131-295 (1955; Zbl 0064.351)]. (2) A general ''inverse limit'' theorem that extends a result of \textit{K. Y. Hu}. Some applications to the construction of Markov processes with regular paths are also discussed.
Mathematics Subject Classification ID: 60G05
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60J45
zbMATH DE Number: 4007352
zbMATH Keywords: projective systems of measures
zbMATH Keywords: stochastic processes with a random parameter set
zbMATH Keywords: random open convex subset
zbMATH Keywords: construction of Markov processes with regular paths
reviewed by: David Nualart
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4007352