Optimal Control of a Stochastic Processing System Driven by a Fractional Brownian Motion Input

Optimal Control of a Stochastic Processing System Driven by a Fractional Brownian Motion Input

We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an ON–OFF input process. We study stochastic control problems associated with the long-run average cost, the infinite-horizondiscounted cost, and thefinite-horizon cost. In addition, wefind a solution to a constrained minimization problem as an applicati...

Optimal control of a stochastic network driven by a fractional Brownian motion input

We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an ON-OFF input process. We study stochastic control problems associated with the long-run average cost, the infinite horizon discounted cost, and the finite horizon cost. In addition, we find a solution to a constrained minimization problem as an applic...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

A singular stochastic differential equation driven by fractional Brownian motion∗

In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter H > 1 2 . Under some assumptions on the drift, we show that there is a unique solution, which has moments of all orders. We also apply the techniques of Malliavin calculus to prove that the solution has an absolutely continuous law at any time t > 0.

Stochastic Differential Equations Driven by a Fractional Brownian Motion

We study existence, uniqueness and regularity of some sto-chastic diierential equations driven by a fractional Brownian motion of any Hurst index H 2 (0; 1): 1. Introduction Fractional Brownian motion and other longgrange dependent processes are more and more studied because of their potential applications in several elds like telecommunications networks, nance markets, biology and so on The ma...