Perturbation theory for fractional Brownian motion in presence of absorbing boundaries
Perturbation theory for fractional Brownian motion in presence of absorbing boundaries
Fractional Brownian motion is a Gaussian process $x(t)$ with zero mean and two-time correlations $\ensuremath{\langle}x({t}_{1})x({t}_{2})\ensuremath{\rangle}=D({t}_{1}^{2H}+{t}_{2}^{2H}\ensuremath{-}|{t}_{1}\ensuremath{-}{t}_{2}|{}^{2H})$, where $H$, with $0<H<1$, is called the Hurst exponent. For $H=1/2$, $x(t)$ is a Brownian motion, while for $H\ensuremath{\ne}1/2$, $x(t)$ is a non-Markovian process. Here we study $x(t)$ in presence of an absorbing boundary at …