The Annals of Probability

Pathwise uniqueness for a degenerate stochastic differential equation

Richard F. Bass, Krzysztof Burdzy, and Zhen-Qing Chen

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We introduce a new method of proving pathwise uniqueness, and we apply it to the degenerate stochastic differential equation


where Wt is a one-dimensional Brownian motion and α∈(0, 1/2). Weak uniqueness does not hold for the solution to this equation. If one restricts attention, however, to those solutions that spend zero time at 0, then pathwise uniqueness does hold and a strong solution exists. We also consider a class of stochastic differential equations with reflection.

Article information

Ann. Probab., Volume 35, Number 6 (2007), 2385-2418.

First available in Project Euclid: 8 October 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60J60: Diffusion processes [See also 58J65]

Pathwise uniqueness weak uniqueness local times stochastic differential equations


Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing. Pathwise uniqueness for a degenerate stochastic differential equation. Ann. Probab. 35 (2007), no. 6, 2385--2418. doi:10.1214/009117907000000033.

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