A stochastic differential equation involving cylindrical 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.

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

Stochastic Differential Equations for Sticky Brownian Motion

dXt = 12 d` 0 t (X) + I(Xt >0) dBt I(Xt =0) dt = 1 2μ d` 0 t (X) for reflecting Brownian motion X in IR+ sticky at 0 , where X starts at x in the state space, μ ∈ (0,∞) is a given constant, `(X) is the local time of X at 0 , and B is a standard Brownian motion. We prove that both systems (i) have a jointly unique weak solution and (ii) have no strong solution. The latter fact verifies Skorokhod...

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...

Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the c...