1. Discrete-Event Stochastic Systems Recall our previous definition of a discrete-event stochastic system: the system makes stochastic state transitions only at an increasing sequence of random times. If X(t) is the state of the system at time t, then a typical sample path of the underlying stochastic process of the simulation, i.e. (X(t): t ≥ 0), looks like this (for a finite or countably infi...

We shall deal only with processes which evolve at discrete instances of time. Typically, the time index can be k0, k0 + 1, . . . , N , with k0 and N both finite, or it can be the nonnegative integers Z+ = 0, 1, . . ., or it can be all the integers Z. Let T be such an index set, which can be finite or countably infinite. Assume also that there is an underlying probability space (Ω,S, P ) with re...

Recently, sliding mode control method has been extended to accommodate stochastic systems. However, the existing results employ an assumption that may be too restrictive for many stochastic systems. This paper aims to remove this assumption and present in terms of LMIs a slidingmode control designmethod for stochastic systems with state delay. In some cases, the proposed method provides a contr...

In the present article, we focus on the numerical approximation of stochastic partial differential equations of Itˆo type with space-time white noise process, in particular, parabolic equations. For each case of additive and multiplicative noise, the numerical solution of stochastic diffusion equations is approximated using two stochastic finite difference schemes and the stability and consiste...