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

Wei Mao, Liangjian Hu, Xuerong Mao

Research output: Contribution to journalArticle

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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.

Original languageEnglish
Pages (from-to)883-896
Number of pages14
JournalApplied Mathematics and Computation
Volume268
Early online date20 Jul 2015
DOIs
Publication statusPublished - 1 Oct 2015

Keywords

  • almost surely asymptotic estimations
  • existence and uniqueness
  • exponential estimations
  • Lévy jumps
  • stochastic pantograph differential equations

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