Existence of solutions and approximate controllability of impulsive fractional stochastic differential systems with infinite delay and Poisson jumps

Chinnathambi Rajivganthi; Krishnan Thiagu; Palanisamy Muthukumar; Pagavathigounder Balasubramaniam

Applications of Mathematics (2015)

  • Volume: 60, Issue: 4, page 395-419
  • ISSN: 0862-7940

Abstract

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The paper is motivated by the study of interesting models from economics and the natural sciences where the underlying randomness contains jumps. Stochastic differential equations with Poisson jumps have become very popular in modeling the phenomena arising in the field of financial mathematics, where the jump processes are widely used to describe the asset and commodity price dynamics. This paper addresses the issue of approximate controllability of impulsive fractional stochastic differential systems with infinite delay and Poisson jumps in Hilbert spaces under the assumption that the corresponding linear system is approximately controllable. The existence of mild solutions of the fractional dynamical system is proved by using the Banach contraction principle and Krasnoselskii's fixed-point theorem. More precisely, sufficient conditions for the controllability results are established by using fractional calculations, sectorial operator theory and stochastic analysis techniques. Finally, examples are provided to illustrate the applications of the main results.

How to cite

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Rajivganthi, Chinnathambi, et al. "Existence of solutions and approximate controllability of impulsive fractional stochastic differential systems with infinite delay and Poisson jumps." Applications of Mathematics 60.4 (2015): 395-419. <http://eudml.org/doc/271586>.

@article{Rajivganthi2015,
abstract = {The paper is motivated by the study of interesting models from economics and the natural sciences where the underlying randomness contains jumps. Stochastic differential equations with Poisson jumps have become very popular in modeling the phenomena arising in the field of financial mathematics, where the jump processes are widely used to describe the asset and commodity price dynamics. This paper addresses the issue of approximate controllability of impulsive fractional stochastic differential systems with infinite delay and Poisson jumps in Hilbert spaces under the assumption that the corresponding linear system is approximately controllable. The existence of mild solutions of the fractional dynamical system is proved by using the Banach contraction principle and Krasnoselskii's fixed-point theorem. More precisely, sufficient conditions for the controllability results are established by using fractional calculations, sectorial operator theory and stochastic analysis techniques. Finally, examples are provided to illustrate the applications of the main results.},
author = {Rajivganthi, Chinnathambi, Thiagu, Krishnan, Muthukumar, Palanisamy, Balasubramaniam, Pagavathigounder},
journal = {Applications of Mathematics},
keywords = {approximate controllability; fixed-point theorem; fractional stochastic differential system; Hilbert space; Poisson jumps; approximate controllability; fixed-point theorem; fractional stochastic differential system; Hilbert space; Poisson jumps},
language = {eng},
number = {4},
pages = {395-419},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of solutions and approximate controllability of impulsive fractional stochastic differential systems with infinite delay and Poisson jumps},
url = {http://eudml.org/doc/271586},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Rajivganthi, Chinnathambi
AU - Thiagu, Krishnan
AU - Muthukumar, Palanisamy
AU - Balasubramaniam, Pagavathigounder
TI - Existence of solutions and approximate controllability of impulsive fractional stochastic differential systems with infinite delay and Poisson jumps
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 4
SP - 395
EP - 419
AB - The paper is motivated by the study of interesting models from economics and the natural sciences where the underlying randomness contains jumps. Stochastic differential equations with Poisson jumps have become very popular in modeling the phenomena arising in the field of financial mathematics, where the jump processes are widely used to describe the asset and commodity price dynamics. This paper addresses the issue of approximate controllability of impulsive fractional stochastic differential systems with infinite delay and Poisson jumps in Hilbert spaces under the assumption that the corresponding linear system is approximately controllable. The existence of mild solutions of the fractional dynamical system is proved by using the Banach contraction principle and Krasnoselskii's fixed-point theorem. More precisely, sufficient conditions for the controllability results are established by using fractional calculations, sectorial operator theory and stochastic analysis techniques. Finally, examples are provided to illustrate the applications of the main results.
LA - eng
KW - approximate controllability; fixed-point theorem; fractional stochastic differential system; Hilbert space; Poisson jumps; approximate controllability; fixed-point theorem; fractional stochastic differential system; Hilbert space; Poisson jumps
UR - http://eudml.org/doc/271586
ER -

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