The existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and L茅vy jumps

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• 作者：Wei Mao ; ^a ; ^{jsjysxx365@126.com" class="auth_mail" title="E-mail the corresponding author} ; Liangjian Hu^b ; Xuerong Mao^c
• 关键词：Stochastic pantograph differential equations ; Lé ; vy jumps ; Existence and uniqueness ; Exponential estimations ; Almost surely asymptotic estimations
• 刊名：Applied Mathematics and Computation
• 出版年：2015
• 出版时间：1 October 2015
• 年：2015
• 卷：268
• 期：Complete
• 页码：883-896
• 全文大小：392 K

文摘

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.