Existence, uniqueness and stability results for impulsive stochastic functional differential equations with infinite delay and poisson jumps

A.Anguraj1* and K.Banupriya2

doi:10.26637/MJM0504/0007

Existence, uniqueness and stability results for impulsive stochastic functional differential equations with infinite delay and poisson jumps

Authors :

A.Anguraj^1* and K.Banupriya²

Author Address :

¹Department of Mathematics, PSG College of Arts and Science, Coimbatore-14 , Tamil Nadu, India.
²Department of Mathematics with CA, PSG College of Arts and Science, Coimbatore-14 , Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper, we study the existence and uniqueness of mild solutions of impulsive stochastic functional differential equations with infinite delay and Poisson jumps under non-Lipschitz condition with Lipschitz condition being considered as a special case by means of the successive approximation. Further, We study the continuous dependence of solutions on the initial value by means of a corollary of the Bihari inequality.

Keywords :

Stochastic differential equations, continuous dependence, Poisson process, impulsive system.

DOI :

10.26637/MJM0504/0007

Article Info :

Received : June 23, 2017; Accepted : September 09, 2017.