The Annals of Probability

Some Examples of Nonlinear Diffusion Processes Having a Time-Periodic Law

Michael Scheutzow

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Abstract

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.

Article information

Source
Ann. Probab., Volume 13, Number 2 (1985), 379-384.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992997

Digital Object Identifier
doi:10.1214/aop/1176992997

Mathematical Reviews number (MathSciNet)
MR781411

Zentralblatt MATH identifier
0563.60066

JSTOR
links.jstor.org

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 60J60: Diffusion processes [See also 58J65] 35B10: Periodic solutions 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Nonlinear diffusion process process with periodic law Ornstein-Uhlenbeck process nonlinear PDE

Citation

Scheutzow, Michael. Some Examples of Nonlinear Diffusion Processes Having a Time-Periodic Law. Ann. Probab. 13 (1985), no. 2, 379--384. doi:10.1214/aop/1176992997. https://projecteuclid.org/euclid.aop/1176992997


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