we focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of it¨o type, in particular, parabolic equations. the main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

We apply multi-scale analysis to stochastic delay-differential equations, deriving approximate stochastic equations for the amplitudes of oscillatory solutions near critical delays of deterministic systems. Such models are particularly sensitive to noise when the system is near a critical point, which marks a transition to sustained oscillatory behavior in the deterministic system. In particula...

in this paper, we present an application of the stochastic calculusto the problem of modeling electrical networks. the filtering problem have animportant role in the theory of stochastic differential equations(sdes). in thisarticle, we present an application of the continuous kalman-bucy filter for a rlcircuit. the deterministic model of the circuit is replaced by a stochastic model byadding a ...

we focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of it¨o type, in particular, parabolic equations. the main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

It is known that optimal stopping problems form an important class of optimal control problems having applications in stochastic calculus (maximal inequalities), statistics (sequential analysis) and mathematical finance (American options). The results about the relationship between optimal stopping problems for Markov processes and free-boundary problems for partial differential equations often...

the edge detour index polynomials were recently introduced for computing theedge detour indices. in this paper we nd relations among edge detour polynomials for the2-dimensional graph of tuc4c8(s) in a euclidean plane and tuc4c8(s) nanotorus.

Abstract: In this paper we discuss stochastic differential delay equations with Markovian switching. Such an equation can be regarded as the result of several stochastic differential delay equations switching from one to the others according to the movement of a Markov chain. The main aim of this paper is to investigate the robustness of exponential stability of the equations. The criteria obta...

Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...