Systems of differential equations modeling non-Markov processes

Markov processes and parabolic partial differential equations

In the first part of this article, we present the main tools and definitions of Markov processes’ theory: transition semigroups, Feller processes, infinitesimal generator, Kolmogorov’s backward and forward equations and Feller diffusion. We also give several classical examples including stochastic differential equations (SDEs) and backward SDEs (BSDEs). The second part of this article is devote...

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Feynman-kac Formulas, Backward Stochastic Differential Equations and Markov Processes

In this paper we explain the notion of stochastic backward differential equations and its relationship with classical (backward) parabolic differential equations of second order. The paper contains a mixture of stochastic processes like Markov processes and martingale theory and semi-linear partial differential equations of parabolic type. Some emphasis is put on the fact that the whole theory ...

Modeling and Verification of Distributed Systems Using Markov Decision Processes

The Markov Decision Process (MDP) formalism is a well-known mathematical formalism to study systems with unknown scheduling mechanisms or with transitions whose next-state probability distribution is not known with precision. Analysis methods for MDPs are based generally on the identification of the strategies that maximize (or minimize) a target function based on the MDP’s rewards (or costs). ...

Numerical Solutions of Special Class of Systems of Non-Linear Volterra Integro-Differential Equations by a Simple High Accuracy Method