The existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and Lévy jumps

Mao, Wei and Hu, Liangjian and Mao, Xuerong (2015) The existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and Lévy jumps. Applied Mathematics and Computation, 268. pp. 883-896. ISSN 0096-3003

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    Abstract

    In this paper, we consider a class of stochastic pantograph differential equations with Lévy jumps (SPDEwLJs). By using the Burkholder-Davis-Gundy inequality and the Kunita's inequality, we prove the existence and uniqueness of solutions to SPDEwLJs whose coefficients satisfying the Lipschitz conditions and the local Lipschitz conditions. Meantime, we establish the p-th exponential estimations and almost surely asymptotic estimations of solutions to SPDEwLJs.