Stability Criteria of Solutions for Stochastic Set Differential Equations

Stability in Distribution of Numerical Solutions for Stochastic Differential Equations

The numerical methods on stochastic differential equations (SDEs) have been well established. There are several papers that study the numerical stability of SDEs with respect to sample paths or moments. In this paper we study the stability in distribution of numerical solution of SDEs.

Stability criteria of stochastic partial differential equations with variable delays∗

Abstract. Some criteria for the asymptotic stability of nonlinear stochastic partial differential equations with variable delays are presented. A coercivity condition plays the role of an exponential stability criterion. Consequently, under the coercivity condition almost all the trajectories of the nonstationary solutions of the given stochastic system finally tend exponentially to zero. Two e...

Approximate Solutions of Set-Valued Stochastic Differential Equations

In this paper, we consider the problem of approximate solutions of set-valued stochastic differential equations. We firstly prove an inequality of set-valued Itô integrals, which is related to classical Itô isometry, and an inequality of set-valued Lebesgue integrals. Both of the inequalities play an important role to discuss set-valued stochastic differential equations. Then we mainly state th...

Stability results for set solution of fuzzy integro-differential systems

Stability Theory for Set Differential Equations

The formulation of set differential equations has an intrinsic disadvantage that the diameter of the solution is nondecreasing as time increases and therefore the behavior of solutions, in some cases, do not match with the solutions of ordinary differential equations from which set differential equations can be generated. In this paper an approach is provided to remove the disadvantage.