Under the condition that the coefficients are Lipschitz continuous, we study the infinitesimal generator of Markov semigroup corresponding to the multivalued stochastic equation. In order to provide a core of the infinitesimal generator, we investigate the associated multivalued elliptic equation and its viscosity solutions.
The project was supported by the Belt and Road National Talent Training base Project for International Cooperation and Exchanges (Grant No. 106052961805), the Zhejiang Provincial Natural Science Foundation (Grant No. LQ13A010020) and the National Natural Science Foundation of China (Grant No. 11471340).
XU Siyan,ZHENG Mengqi. The Infinitesimal Generator of Markov Semigroup Associated with Multivalued Stochastic Differential Equation[J]. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2018, 34(6): 565-576.