Pathwise uniqueness for a degenerate stochastic differential equation
Bass, Richard F. ; Burdzy, Krzysztof ; Chen, Zhen-Qing
Ann. Probab., Tome 35 (2007) no. 1, p. 2385-2418 / Harvested from Project Euclid
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We introduce a new method of proving pathwise uniqueness, and we apply it to the degenerate stochastic differential equation ¶ dXt=|Xt|α dWt, ¶ 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.
Publié le : 2007-11-14
Classification:  Pathwise uniqueness,  weak uniqueness,  local times,  stochastic differential equations,  60H10,  60J60 
@article{1191860425,
     author = {Bass, Richard F. and Burdzy, Krzysztof and Chen, Zhen-Qing},
     title = {Pathwise uniqueness for a degenerate stochastic differential equation},
     journal = {Ann. Probab.},
     volume = {35},
     number = {1},
     year = {2007},
     pages = { 2385-2418},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1191860425}
}

Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing. Pathwise uniqueness for a degenerate stochastic differential equation. Ann. Probab., Tome 35 (2007) no. 1, pp.  2385-2418. http://gdmltest.u-ga.fr/item/1191860425/