Time fractional stochastic differential equations driven by pure jump Levy noise

[摘要] In this paper we introduce a variable order time fractional differential equation driven by pure jump Levy noise, which models the motion of a particle exhibiting memory effect. We prove the well-posedness of this equation without assuming any integrability condition on the initial condition and the large jump coefficient, by using a truncation argument. Under some extra conditions, we also derive some L-p moment estimates on the solutions. As an application of moment estimates, we prove the Holder regularity of the solutions. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-15

[关键词] Variable-order;Time fractional stochastic differential equation;Well-posedness;Moment estimates;Regularity