Numerical Stability Analysis of Stochastic Delay Differential Equations

Abstract

This thesis mainly concerned with the stability analysis of nu me r. L c {i [ methods ft-Pr stochastic delay differential equations, Stochastic diffettntizil equations many times result in modeling of problems I i ke population dynamics. financial and neural networks etc, In many situations the explicit form of the solutions of such equations cannot kbe acquired, This thesis analyses the stability of numerical methods for stochastic delay HoptieId neural networks, This thesis consists of four parts. The first one 4.4 this thesis is the study of mean square stability of two step Maruyama methods of stochastic delay HopfieId neural networks, The second one of the thesis is the study of the almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neuriAl networks. The third chapicr or the thesis is a study about the trajectory stabilbty of numenczll methods of stochastic delay Hopfield neural networks, The last chapter of the thesis deals the T-stability of two-step Maruyarna methods of stochastic delay Hoptield neural networks.