Superdiffusion and parabolic nonlinear differential equations
type: Item
instance of: scholarly article
title: Superdiffusion and parabolic nonlinear differential equations
zbMATH Open document ID: 0756.60074
author: E. B. Dynkin
published in: The Annals of Probability
publication date: 1993-01-16T00:00:00Z
review text: The model under consideration is a \(d\)-dimensional superdiffusion \(X\) with parameters \((L,\alpha)\); that is, \(X\) is related to the parabolic differential equation \((\partial/\partial r)\nu+L\nu-|\nu|^ \alpha=-\rho\). Here \(1<\alpha\leq 2\), and \(L\) is a ``uniformly'' elliptic differential operator with bounded and sufficiently ``smooth'' coefficients (depending on time and space). Connections between \(X\) and that equation are established, especially concerning their minimal and maximal positive solutions. Analytic results are used to study the graph \({\mathcal G}\) of \(X\). In particular, a \({\mathcal G}\)-polar set is characterized as an analytic set of capacity 0 in the sense of \textit{N. G. Meyers} [Math. Scand. 26, 255-292 (1971; Zbl 0242.31006)].
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 89796
zbMATH Keywords: graph of a superprocess
zbMATH Keywords: capacities
zbMATH Keywords: polar sets
zbMATH Keywords: superdiffusion
zbMATH Keywords: parabolic differential equation
zbMATH Keywords: minimal and maximal positive solutions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176989812
OpenAlex ID: W1996586731
DOI: 10.1214/AOP/1176989812
description: scientific article; zbMATH DE number 89796