Path integral formulation of fractional Brownian motion for general Hurst exponent

Abstract

In J. Phys. A: Math. Gen. 28, 4305 (1995), K. L. Sebastian gave a path integral computation of the propagator of subdiffusive fractional Brownian motion (fBm), i.e. fBm with a Hurst or self-similarity exponent $H\in(0,1/2)$. The extension of Sebastian's calculation to superdiffusion, $H\in(1/2,1]$, becomes however quite involved due to the appearance of additional boundary conditions on fractional derivatives of the path. In this paper, we address the construction of the path integral representation in a different fashion, which allows to treat both subdiffusion and superdiffusion on an equal footing. The derivation of the propagator of fBm for general Hurst exponent is then performed in a neat and unified way.

6 pages. Published version