In this paper we present an Lp-theory for a class of stochastic partial differential equations (SPDEs in abbreviation) driven by Lévy processes. The SPDEs under consideration can have random coefficients that depend both on the time and space variable. Existence and uniqueness of solutions in various Sobolev spaces are obtained. These Sobolev spaces describe the regularity of the solutions of the SPDEs.
Bibliographical noteFunding Information:
The research of Zhen-Qing Chen is supported in part by NSF Grants DMS-0906743 and DMR-1035196. The research of Kyeong-Hun Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology(20110015961).
© de Gruyter 2014.
- Lévy process
- Sobolev space
- Stochastic partial differential equation
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics