Abstract
In this paper, we study the existence and uniqueness of solutions for several classes of stochastic evolution equations with non-Lipschitz coefficients, that contains backward stochastic evolution equations, stochastic Volterra type evolution equations and stochastic functional evolution equations. In particular, the results can be used to treat a large class of quasi-linear stochastic equations, which includes the reaction diffusion and porous medium equations.
| Original language | English |
|---|---|
| Pages (from-to) | 549-595 |
| Number of pages | 47 |
| Journal | Stochastics and Dynamics |
| Volume | 9 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Dec 2009 |
| Externally published | Yes |
Keywords
- Backward stochastic evolution equation
- Stochastic evolution equation
- Stochastic functional integral evolution equation
- Stochastic porous medium equation
- Stochastic reaction diffusion equation