Stochastic representation of subdiffusion processes with time-dependent drift

Marcin Magdziarz ()

Stochastic Processes and their Applications, 2009, vol. 119, issue 10, 3238-3252

Abstract: 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.

Keywords: Subdiffusion; Inverse; subordinator; First-passage; time; [alpha]-stable; distribution; Fractional; Fokker-Planck; equation (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (22)

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