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June, 1975 Transience and Solvability of a Non-Linear Diffusion Equation
Stephen L. Portnoy
Ann. Probab. 3(3): 465-477 (June, 1975). DOI: 10.1214/aop/1176996353

Abstract

This paper is concerned with the existence of bounded solutions to an operator inequality which is a non-linear version of a discrete time diffusion equation. Here, the solvability of the inequality will be closely related to the transience of a corresponding random walk. In particular, the inequality will generally be solvable in three or more dimensions, but not in one or two dimensions if appropriate moment conditions hold.

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Stephen L. Portnoy. "Transience and Solvability of a Non-Linear Diffusion Equation." Ann. Probab. 3 (3) 465 - 477, June, 1975. https://doi.org/10.1214/aop/1176996353

Information

Published: June, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0309.60043
MathSciNet: MR394889
Digital Object Identifier: 10.1214/aop/1176996353

Subjects:
Primary: 60J15
Secondary: 47H15 , 60G50 , 60J60

Keywords: Admissibility , Non-linear diffusion equation , Random walk

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 3 • June, 1975
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