Stochastic differential equations with Markovian switching (SDEwMSs), one of the important classes of hybrid systems, have been used to model many physical systems that are subject to frequent unpredictable structural changes. The research in this area has been both theoretical and applied. Although the numerical methods for stochastic differential equations (SDEs) have been well studied, there...

In this section is presented the stochastic SIS epidemic model for a closed environment. The order of exposition is the following: firstly is presented the deterministic SI epidemic model, secondly is presented the stochastic SI epidemic model, thirdly is presented the deterministic SIS epidemic model and finally is presented the stochastic SIS epidemic model. All these epidemic models are form...

We consider a stochastic version of the basic predator-prey differential equation model. The model, which contains a parameter ω which represents the number of individuals for one unit of prey If x denotes the quantity of prey in the differential equation model x = 1 means that there are ω individuals in the discontinuous one is derived from the classical birth and death process. It is shown by...

in this current study a generalized super-efficiency model is first proposed for ranking extreme efficient decision making units (dmus) in stochastic data envelopment analysis (dea) and then, a deterministic (crisp) equivalent form of the stochastic generalized super-efficiency model is presented. it is shown that this deterministic model can be converted to a quadratic programming model. so fa...

A stochastic differential equation model is considered for nonlinear oscillators under excitations of combined Gaussian and Poisson white noise. Since the solutions of stochastic differential equations can be interpreted in terms of several types of stochastic integrals, it is sometimes confusing about which integral is actually appropriate. In order for the energy conservation law to hold unde...

In this paper, stability theorems for stochastic differential equations and backward stochastic differential equations driven by G-Brownian motion are obtained. We show the existence and uniqueness of solutions to forward-backward stochastic differential equations driven by G-Brownian motion. Stability theorem for forward-backward stochastic differential equations driven by G-Brownian motion is...

Phase noise is one of the main impairments in wireless communications systems, due to its strong distortion of the transmitted signal. In this work, a discrete time phase noise model for simulation environments is proposed. This model can be used to obtain a better understanding of the effects of phase noise on the behavior of communications systems. It has already been shown that phase noise c...