Time fractional equations and probabilistic representation

In this paper, we study the existence and uniqueness of solutions for general fractional-time parabolic equations of mixture type, and their probabilistic representations in terms of the corresponding inverse subordinators with or without drifts. An explicit relation between occupation measure for M...

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Bibliographic Details
Published inChaos, solitons and fractals Vol. 102; pp. 168 - 174
Main Author Chen, Zhen-Qing
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2017
Subjects
Fractional-time derivative
Inverse subordinator
Lévy measure
Occupation measure
Subordinator
Primary 26A33
60H30
Secondary: 34K37
Lévy measure
Subordinator
Occupation measure
Inverse subordinator
Fractional-time derivative
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Summary:In this paper, we study the existence and uniqueness of solutions for general fractional-time parabolic equations of mixture type, and their probabilistic representations in terms of the corresponding inverse subordinators with or without drifts. An explicit relation between occupation measure for Markov processes time-changed by inverse subordinator in open sets and that of the original Markov process in the open set is also given.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2017.04.029