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.
Citation
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
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