JACOBI PROCESSES DRIVEN BY FRACTIONAL BROWNIAN MOTION

Maxima of stochastic processes driven by fractional Brownian motion

We study stationary processes given as solutions to SDEs driven by fractional Brownian motion (FBM). This class includes the fractional Ornstein-Uhlenbeck process (FOUP), but is a much richer class of processes, which can be obtained by state space transformations of the FOUP. An explicit formula in terms of Euler’s Γ-function describes the asymptotic behaviour of the covariance function of FOU...

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

Some Properties of Fractional Bessel Processes Driven by Fractional Brownian Motion

Fractional Bessel processes are defined and considering the processes associated with fractional Bessel processes 1 2 1 ), ( )) ( ( ) ( 0 < < = ∫ H t dB s B sign t X H t H H ) ( ) ( ) ( 1 0 s dB s R B t Y j H d

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

Flow properties of differential equations driven by fractional Brownian motion

We prove that solutions of stochastic differential equations driven by fractional Brownian motion for H > 1/2 define flows of homeomorphisms on R. AMS Subject Classification: 60H05, 60H07