Stochastic representation of a fractional subdiffusion equation. The case of infinitely divisible waiting times, Lévy noise and space-time-dependent coefficients. (English) Zbl 1335.60126
The authors state some results on the stochastic representation of a Fokker-Planck-Kolmogorov equation associated with a fractional subdivision process. It is shown that, in many cases, the corresponding process can be defined by a Langevin equation driven by Brownian motion and Lévy noise. This result provides new approaches to derive approximate solutions for fractional FPK equations using Monte Carlo methods.
Reviewer: Guy Jumarie (Montréal)
MSC:
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 60J60 | Diffusion processes |
| 35Q84 | Fokker-Planck equations |
| 35R11 | Fractional partial differential equations |
| 60G51 | Processes with independent increments; Lévy processes |
| 60J65 | Brownian motion |
| 65C05 | Monte Carlo methods |
Keywords:
fractional subdiffusion equation; Fokker-Planck-Kolmogorov equation; fractional subdivision; Langevin equation; Lévy noise; Brownian motion; Monte Carlo methodsReferences:
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