Stochastic representation of subdiffusion processes with time-dependent drift

In statistical physics, subdiffusion processes are characterized by certain power-law deviations from the classical Brownian linear time dependence of the mean square displacement. For the mathematical description of subdiffusion, one uses fractional Fokker-Planck equations. In this paper we construct a stochastic process, whose probability density function is the solution of the fractional Fokker-Planck equation with time-dependent drift. We propose a strongly and uniformly convergent approximation scheme which allows us to approximate solutions of the fractional Fokker-Planck equation using Monte Carlo methods. The obtained results for moments of stochastic integrals driven by the inverse [alpha]-stable subordinator play a crucial role in the proofs, but may be also of independent interest.