Fractional backward Kolmogorov equations

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 solu...

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Bibliographic Details
Published inChinese physics B Vol. 21; no. 6; pp. 1 - 5
Main Author 张红 李国华 罗懋康
Format Journal Article
LanguageEnglish
Published 01.06.2012
Subjects
Construction
Differential equations
Dynamics
Fractal analysis
Fractals
Kolmogorov
Mathematical analysis
Mathematical models
Probability density functions
Stochasticity
分形空间
分数
反时限
时间
柯尔莫哥洛夫
概率密度函数
随机微分方程
Online AccessGet full text
ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/21/6/060201

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Summary: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（Sα （t））, the subordinator Sα （t） is termed as the inverse-time a-stable subordinator and the process X（τ） satisfies the corresponding time homogeneous Ito stochastic differential equation.
Bibliography:Zhang Hong, Li Guo-Hua, and Luo Mao-Kang（College of Mathematics, Sichuan University, Chengdu 610064, China）
anomalous diffusive, fractional backward Kolmogorov equations, subordinated process
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（Sα （t））, the subordinator Sα （t） is termed as the inverse-time a-stable subordinator and the process X（τ） satisfies the corresponding time homogeneous Ito stochastic differential equation.
11-5639/O4
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ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/21/6/060201