Abstract
Using the Wiener chaos decomposition, we show that strong solutions of non-Lipschitzian stochastic differential equations are given by random Markovian kernels. The example of Sobolev flows is studied in some detail, exhibiting interesting phase transitions.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 826-873 |
| Number of pages | 48 |
| Journal | Annals of Probability |
| Volume | 30 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 2002 |
Keywords
- Coalescence
- Dirichlet form
- Isotropic Brownian flow
- Stochastic differential equations
- Stochastic flow
- Strong solution
- Wiener chaos decomposition
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty