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.
Publié le : 1975-06-14
Classification:
Non-linear diffusion equation,
random walk,
admissibility,
60J15,
60J60,
47H15,
60G50
@article{1176996353,
author = {Portnoy, Stephen L.},
title = {Transience and Solvability of a Non-Linear Diffusion Equation},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 465-477},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996353}
}
Portnoy, Stephen L. Transience and Solvability of a Non-Linear Diffusion Equation. Ann. Probab., Tome 3 (1975) no. 6, pp. 465-477. http://gdmltest.u-ga.fr/item/1176996353/