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November 2007 Pathwise uniqueness for a degenerate stochastic differential equation
Richard F. Bass, Krzysztof Burdzy, Zhen-Qing Chen
Ann. Probab. 35(6): 2385-2418 (November 2007). DOI: 10.1214/009117907000000033

Abstract

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

dXt=|Xt|αdWt,

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.

Citation

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Richard F. Bass. Krzysztof Burdzy. Zhen-Qing Chen. "Pathwise uniqueness for a degenerate stochastic differential equation." Ann. Probab. 35 (6) 2385 - 2418, November 2007. https://doi.org/10.1214/009117907000000033

Information

Published: November 2007
First available in Project Euclid: 8 October 2007

zbMATH: 1139.60027
MathSciNet: MR2353392
Digital Object Identifier: 10.1214/009117907000000033

Subjects:
Primary: 60H10
Secondary: 60J60

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 6 • November 2007
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