In this paper it is shown that contrary to "linear" homogeneous nondegenerate diffusion processes, "nonlinear" diffusion processes can have a time-periodic law. We study four qualitatively different simple examples: a law-dependent Ornstein-Uhlenbeck process, a deterministic example, a one-dimensional example with a "semilinear" drift and a two-dimensional example with a linear drift.
Publié le : 1985-05-14
Classification:
Nonlinear diffusion process,
process with periodic law,
Ornstein-Uhlenbeck process,
nonlinear PDE,
35K55,
60J60,
35B10,
60H10
@article{1176992997,
author = {Scheutzow, Michael},
title = {Some Examples of Nonlinear Diffusion Processes Having a Time-Periodic Law},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 379-384},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992997}
}
Scheutzow, Michael. Some Examples of Nonlinear Diffusion Processes Having a Time-Periodic Law. Ann. Probab., Tome 13 (1985) no. 4, pp. 379-384. http://gdmltest.u-ga.fr/item/1176992997/