Stochastic Differential Equations driven by Fractional Brownian Motion with Markovian Switching

Abstract

Two circles of ideas permeate a great deal of the specialized literature on stochastic modelling nowadays: that which study long-range dependence phenomena, with particular emphasis on fractional Brownian motion, and the one which considers stochastic dif- ferential equations with Markov switching. In this paper we put together these topics by analysing a class of stochastic differential equations with Markov switching and subject to a fractional Brownian motion perturbation. We prove global existence and uniqueness results for this class of stochastic equations. This, in turn, set the stage for an avenue of research associated with this class of models which seems promising; particularly that associated with control problems.