Banupriya, K and Abinaya, S (2020) NEUTRAL IMPULSIVE STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH FINITE DELAY AND POISSON JUMPS. Journal of Fractional Calculus and Applications, 11 (1). pp. 11-21. ISSN 2090-5858

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Abstract

Impulsive stochastic differential equations are effectively used to describe
the real life phenomena in the fields of ecology, chemical technology, electrical engineering, etc. So many researchers showed interest in investigating neutral stochastic
differential equations. ( Refer [10], [12], [4],[11])
Fractional Brownian motions are widely used in modelling many complex phenomena in applications when the systems are subject to rough external forcing.
An fbm is differs from the standard Brownian motion, semi-martingales and others
classically used in the theory of stochastic processes. It is a family of centered
Gaussian processes with continuous sample paths indexed by the Hurst parameter H ∈ (0, 1). It is a self similar process with stationary increments and has a
long-memory when H > 1
2
.
Initially, Ferrante and Rovira established the existence and uniqueness of solutions to delayed SDEs with fbm for H > 1
2
and constant delay by using the
skorohod integral based on the malliavin calculus [5]. Existence and continuability of solutions for differential equations with delays and state-dependent impulses
is established by Xinzhi Liu and George Ballinger [16]. Many researchers studied
equations driven by fractional Brownian motion ( [1], [6], [8], [13]). Stochastic differential equations with Poisson jumps have been considered by many authors ([4],
[3], [7], [9]). Caraballo.et.al have studied the existence, uniqueness and exponential
asymptotic behaviour of mild solutions by using wiener integral [2]. Nguyen Tien Dung studied existence, uniqueness and exponential stability of neutral stochastic
differential equations using Banach-fixed point theory[14].

Item Type: Article
Uncontrolled Keywords: Stochastic differential equations, fractional brownian motion, finite delay, contraction mapping principle, Banach fixed point theorem
Divisions: PSG College of Arts and Science > Department of Mathematics
Depositing User: Mr Team Mosys
Date Deposited: 17 Nov 2022 06:18
Last Modified: 17 Nov 2022 06:18
URI: http://ir.psgcas.ac.in/id/eprint/1633

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