Fractional backward Kolmogorov equations

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

中国物理B ›› 2012, Vol. 21 ›› Issue (6): 60201-060201.doi: 10.1088/1674-1056/21/6/060201

• GENERAL • 下一篇

Fractional backward Kolmogorov equations

张红, 李国华, 罗懋康

College of Mathematics, Sichuan University, Chengdu 610064, China

收稿日期:2012-01-09 修回日期:2012-02-15 出版日期:2012-05-01 发布日期:2012-05-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11171238).

Fractional backward Kolmogorov equations

Zhang Hong(张红), Li Guo-Hua(李国华), and Luo Mao-Kang(罗懋康)^†

College of Mathematics, Sichuan University, Chengdu 610064, China

Received:2012-01-09 Revised:2012-02-15 Online:2012-05-01 Published:2012-05-01
Contact: Luo Mao-Kang E-mail:makaluo@scu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11171238).

摘要/Abstract

摘要： 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.

关键词: anomalous diffusive, fractional backward Kolmogorov equations, subordinated process

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.

Key words: anomalous diffusive, fractional backward Kolmogorov equations, subordinated process

中图分类号: (Probability theory, stochastic processes, and statistics)

02.50.-r

05.30.Pr (Fractional statistics systems) 05.10.Gg (Stochastic analysis methods)

张红, 李国华, 罗懋康. Fractional backward Kolmogorov equations[J]. 中国物理B, 2012, 21(6): 60201-060201.

Zhang Hong(张红), Li Guo-Hua(李国华), and Luo Mao-Kang(罗懋康) . Fractional backward Kolmogorov equations[J]. Chin. Phys. B, 2012, 21(6): 60201-060201.

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Fractional backward Kolmogorov equations

Fractional backward Kolmogorov equations

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