Stochastic bifurcation models

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paper65.pdf (378.14 KB)

Date

1999-01

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Burdzy, Krzysztof
Bass, Richard F.

Journal Title

Journal ISSN

Volume Title

Publisher

Institute of Mathematical Statistics

Abstract

We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of bifurcation. A relationship with Lipschitz approximations to Brownian paths is also discussed.

Description

Keywords

Brownian motion, fractional Brownian motion, differential equations, stochastic differential equations, local time, Trotter theorem, Ray-Knight theorem, Lipschitz approximation, bifurcation, bifurcation time

Citation

Bass, R.F. & K. Burdzy. (1999). Stochastic bifurcation models. Annals of Probability, 27(1): 50-108.

URI

http://hdl.handle.net/1773/2197

DOI

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EPrint Collection - Mathematics