Stochastic integrals and stochastic differential equations with respect to the fractional Brownian field

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

Stochastic integration with respect to the fractional Brownian motion

We develop a stochastic calculus for the fractional Brownian motion with Hurst parameter H > 2 using the techniques of the Malliavin calclulus. We establish estimates in Lp, maximal inequalities and a continuity criterion for the stochastic integral. Finally, we derive an Itô’s formula for integral processes.

existence and measurability of the solution of the stochastic differential equations driven by fractional brownian motion

Stochastic calculus with respect to fractional Brownian motion

— Fractional Brownian motion (fBm) is a centered selfsimilar Gaussian process with stationary increments, which depends on a parameter H ∈ (0, 1) called the Hurst index. In this conference we will survey some recent advances in the stochastic calculus with respect to fBm. In the particular case H = 1/2, the process is an ordinary Brownian motion, but otherwise it is not a semimartingale and Itô...

Volterra Equations with Fractional Stochastic Integrals

We assume that a probability space (Ω,η,P) is given, where Ω denotes the space C(R+, Rk) equipped with the topology of uniform convergence on compact sets, η the Borel σ-field of Ω, and P a probability measure on Ω. Let {Wt(ω) = ω(t), t ≥ 0} be a Wiener process. For any t ≥ 0, we define ηt = σ{ω(s); s < t}∨Z, where Z denotes the class of the elements in ηt which have zero P-measure. Pardoux and...