On the pathwise uniqueness of solutions of stochastic differential equations driven by multi-dimensional symmetric α stable class

Abstract

We will propose a sufficient condition which guarantees the pathwise uniqueness for jump type equations in multi-dimensional case. An example given in Section 3 shows that the condition is nearly best possible. Comparing our results with those known in the case of Brownian equations, we claim that essential difference between these two cases. It seems to be remarkable that we could explain these phenomena in the language of the Potential theory. Our principal method in the paper is based on the Fourier analysis, where effective tools such as Bessel functions, hypergeometric functions play essential roles.