explain stability of stochastic differential equations(sde)?

Question

give definitions for stability & stochastic stability with examples in detail.theorems with proof for exponential,asymptotic,mean-square stability of solutions of sde with relation to ito's integral & with examples in detail.stability of weak & strong solutions of sde.complete introduction to sde

Answer 1

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, thus resulting in a solution which is itself a stochastic process.

i recommend that you read the following books:
Stochastic Differential Equations: An Introduction with Applications by Bernt Oksendal
Stochastic Differential Equations and Applications by Avner Friedman
Stochastic Integration and Differential Equations by Philip E. Protter
these are excelent textbooks.