One dimensional stochastic partial differential equations and the branching measure diffusion
type: Item
instance of: scholarly article
title: One dimensional stochastic partial differential equations and the branching measure diffusion
zbMATH Open document ID: 0651.60069
DOI: 10.1007/BF00340057
author: Mark Reimers
publication date: 1989-01-01T00:00:00Z
review text: An existence theorem in the spirit of \textit{H. J. Keisler} [see: An infinitesimal approach to stochastic analysis. Mem. Am. Math. Soc. 297 (1984; Zbl 0529.60062)], is proved for the simple one-dimensional diffusion equation driven by white noise modulated by a nonlinear function of the solution. This is used to obtain a density and a stochastic partial differential equation in one dimension for the critical branching diffusion studied by \textit{D. A. Dawson} and \textit{K. J. Hochberg} [see Ann. Probab. 7, 693-703 (1979; Zbl 0411.60084), and Carlton Math. Lecture Notes No.22, 4 (1978; Zbl 0381.60044)].
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 4062292
zbMATH Keywords: existence theorem
zbMATH Keywords: critical branching diffusion
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4062292