A new approach to stochastic evolution equations with adapted drift |
| |
Authors: | Matthijs Pronk Mark Veraar |
| |
Affiliation: | Delft Institute of Applied Mathematics, Delft University of Technology, 2600 GA Delft, The Netherlands |
| |
Abstract: | In this paper we develop a new approach to stochastic evolution equations with an unbounded drift A which is dependent on time and the underlying probability space in an adapted way. It is well-known that the semigroup approach to equations with random drift leads to adaptedness problems for the stochastic convolution term. In this paper we give a new representation formula for the stochastic convolution which avoids integration of non-adapted processes. Here we mainly consider the parabolic setting. We establish connections with other solution concepts such as weak solutions. The usual parabolic regularity properties are derived and we show that the new approach can be applied in the study of semilinear problems with random drift. At the end of the paper the results are illustrated with two examples of stochastic heat equations with random drift. |
| |
Keywords: | 60H15 35R60 47D06 |
本文献已被 ScienceDirect 等数据库收录! |