Burdzy, KrzysztofBass, Richard F.Chen, Zhen-Qing2005-12-012005-12-012004-05Bass, R.F., K. Burdzy, & Z.Q. Chen. (2004). Stochastic differential equations driven by stable processes for which pathwise uniqueness fails. Stochastic Processes and Their Applications, 111(1), 1-15.http://hdl.handle.net/1773/2228Let Z [subscript] t be a one-dimensional symmetric stable process of order [alpha] with [alpha is an element of the set] (0, 2) and consider the stochastic differential equation dX [subscript] t = [omega] (X [subscript] t−)dZ [subscript]t. For [beta] < 1 [divided by alpha] ^ 1, we show there exists a function that is bounded above and below by positive constants and which is Holder continuous of order [beta] but for which pathwise uniqueness of the stochastic differential equation does not hold. This result is sharp.179719 bytesapplication/pdfen-USStable processespathwise uniquenessstochastic differential equationstime changecrossing estimatesArticle