TY - JOUR
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
UR - http://www.scopus.com/inward/record.url?scp=84937598246&partnerID=8YFLogxK
UR - http://www.sciencedirect.com/science/article/pii/S0096300315008905
U2 - 10.1016/j.amc.2015.06.109
DO - 10.1016/j.amc.2015.06.109
M3 - Article
AN - SCOPUS:84937598246
SN - 0096-3003
VL - 268
SP - 883
EP - 896
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -