Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps

作     者：PALANISAMY Muthukumar CHINNATHAMBI Rajivganthi 

作者机构：Department of Mathematics Gandhigram Rural Institute-Deemed University 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报(英文版))

年 卷 期：2015年第28卷第5期

页      面：1033-1048页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：supported by the National Board for Higher Mathematics Mumbai India under Grant No.2/48(5)/2013/NBHM(R.P.)/RD-II/688 dt 16.01.2014 

主　　题：Approximate controllability Hilbert space Poisson jumps second-order neutral stochastic differential equations semigroup theory 

摘      要：The modelling of risky asset by stochastic processes with continuous paths, based on Brownian motions, suffers from several defects. First, the path continuity assumption does not seem reasonable in view of the possibility of sudden price variations(jumps) resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.