Fractional backward Kolmogorov equations

doi:10.1088/1674-1056/21/6/060201

Abstract This paper derives the fractional backward Kolmogorov equations in fractal space-time based on the construction of a model for dynamic trajectories. It shows that for the type of fractional backward Kolmogorov equation in the fractal time whose coefficient functions are independent of time, its solution is equal to the transfer probability density function of the subordinated process X(S_α(t)), the subordinator S_α(t) is termed as the inverse-time α-stable subordinator and the process X(τ) satisfies the corresponding time homogeneous Itô stochastic differential equation.

Keywords: anomalous diffusive fractional backward Kolmogorov equations subordinated process

Received: 09 January 2012
Revised: 15 February 2012
Accepted manuscript online:

PACS:	02.50.-r	(Probability theory, stochastic processes, and statistics)
	05.30.Pr	(Fractional statistics systems)
	05.10.Gg	(Stochastic analysis methods)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11171238).

Corresponding Authors: Luo Mao-Kang
E-mail: makaluo@scu.edu.cn

Cite this article:

Zhang Hong(张红), Li Guo-Hua(李国华), and Luo Mao-Kang(罗懋康) Fractional backward Kolmogorov equations 2012 Chin. Phys. B 21 060201

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