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

Wei Mao; Liangjian Hu; Xuerong Mao

doi:10.1016/j.amc.2015.06.109

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

Wei Mao, Liangjian Hu, Xuerong Mao

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7 Citations (Scopus)

40 Downloads (Pure)

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 language	English
Pages (from-to)	883-896
Number of pages	14
Journal	Applied Mathematics and Computation
Volume	268
Early online date	20 Jul 2015
DOIs	https://doi.org/10.1016/j.amc.2015.06.109
Publication status	Published - 1 Oct 2015

Keywords

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

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10.1016/j.amc.2015.06.109

Mao-etal-AMC-2015-The-existence-and-asymptotic-estimations-of-solutions-to-stochastic-pantograph-equationsAccepted author manuscript, 147 KBLicence: CC BY-NC-ND 4.0

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title = "The existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and L{\'e}vy jumps",

abstract = "In this paper, we consider a class of stochastic pantograph differential equations with L{\'e}vy 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.",

keywords = "almost surely asymptotic estimations, existence and uniqueness, exponential estimations, L{\'e}vy jumps, stochastic pantograph differential equations",

author = "Wei Mao and Liangjian Hu and Xuerong Mao",

year = "2015",

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doi = "10.1016/j.amc.2015.06.109",

language = "English",

volume = "268",

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T1 - The existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and Lévy jumps

AU - Mao, Wei

AU - Hu, Liangjian

AU - Mao, Xuerong

PY - 2015/10/1

Y1 - 2015/10/1

N2 - 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.

AB - 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.

KW - almost surely asymptotic estimations

KW - existence and uniqueness

KW - exponential estimations

KW - Lévy jumps

KW - stochastic pantograph differential equations

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DO - 10.1016/j.amc.2015.06.109

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JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

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