Pathwise uniqueness for a degenerate stochastic differential equation
成果类型：
Article
署名作者：
Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing
署名单位：
University of Connecticut; University of Washington; University of Washington Seattle
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117907000000033
发表日期：
2007
页码：
2385-2418
关键词：
摘要：
We introduce a new method of proving pathwise uniqueness, and we apply it to the degenerate stochastic differential equation dX(t) = vertical bar X-t vertical bar(alpha) dW(t), where W-t is a one-dimensional Brownian motion and alpha is an element of (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.