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In J. Phys. A: Math. Gen. 28, 4305 (1995), K. L. Sebastian gave a pathintegral computation of the propagator of subdiffusive fractional Brownianmotion (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 boundaryconditions on fractional derivatives of the path. In this paper, we address theconstruction of the path integral representation in a different fashion, whichallows to treat both subdiffusion and superdiffusion on an equal footing. Thederivation of the propagator of fBm for general Hurst exponent is thenperformed in a neat and unified way.

Path integral formulation of fractional Brownian motion for general Hurst exponent