XU Siyan, ZHENG Mengqi. The Infinitesimal Generator of Markov Semigroup Associated with Multivalued Stochastic Differential Equation[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(6): 565-576. DOI: 10.3969/j.issn.1001-4268.2018.06.002
Citation: XU Siyan, ZHENG Mengqi. The Infinitesimal Generator of Markov Semigroup Associated with Multivalued Stochastic Differential Equation[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(6): 565-576. DOI: 10.3969/j.issn.1001-4268.2018.06.002
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The Infinitesimal Generator of Markov Semigroup Associated with Multivalued Stochastic Differential Equation

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  • 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.
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