The Annals of Probability

Stochastic Bifurcation Models

Richard F. Bass and Krzysztof Burdzy

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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.

Article information

Ann. Probab., Volume 27, Number 1 (1999), 50-108.

First available in Project Euclid: 29 May 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60G17: Sample path properties 60H10: Stochastic ordinary differential equations [See also 34F05]

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


Bass, Richard F.; Burdzy, Krzysztof. Stochastic Bifurcation Models. Ann. Probab. 27 (1999), no. 1, 50--108. doi:10.1214/aop/1022677254.

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