Stochastic differential equations driven by symmetric stable processes. (English) Zbl 1039.60056

Bass, Richard F.

Azéma, Jacques (ed.) et al., 36th seminar on probability. Berlin: Springer (ISBN 3-540-00072-0/pbk). Lect. Notes Math. 1801, 302-313 (2003).

From the introduction: Let \(X\) be a one-dimensional symmetric stable process of index \(\alpha\in (0,2)\). We consider the stochastic differential equation \(dY_t= F(Y_{t-})\,dX_t,\) \(Y_0= x_0.\) We have two main results. Our first is the analogue of the Yamada-Watanabe condition for diffusions. Our second main result covers the case \(\alpha\in (0,1)\).
For the entire collection see [Zbl 1003.00010].

MSC:

60H10

Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

stochastic differential equations; symmetric stable processes