A Sobolev space theory for parabolic stochastic PDEs driven by Levy processes on C-1-domains

作者：Kim Kyeong Hun^*

来源：Stochastic Processes and Their Applications, 2014, 124(1): 440-474.

DOI：10.1016/j.spa.2013.08.008

• Stochastic partial differential equations
• Levy processes
• Sobolev spaces
• L-p-theory

In this paper we study parabolic stochastic partial differential equations (SPDEs) driven by Levy processes defined on R-d, R-+(d) and bounded C-1-domains. The coefficients of the equations are random functions depending on time and space variables. Existence and uniqueness results are proved in (weighted) Sobolev spaces, and L-p-estimates and various properties of solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular it can be negative or fractional.

• 出版日期2014-1