Time fractional equations and probabilistic representation

Zhen Qing Chen

doi:10.1016/j.chaos.2017.04.029

Time fractional equations and probabilistic representation

Zhen Qing Chen

University of Washington

Research output: Contribution to journal › Article › peer-review

64 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	168-174
Number of pages	7
Journal	Chaos, Solitons and Fractals
Volume	102
DOIs	https://doi.org/10.1016/j.chaos.2017.04.029
Publication status	Published - 1 Sept 2017
Externally published	Yes

Keywords

Fractional-time derivative
Inverse subordinator
Lévy measure
Occupation measure
Subordinator

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10.1016/j.chaos.2017.04.029

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Chen, Z. Q. (2017). Time fractional equations and probabilistic representation. Chaos, Solitons and Fractals, 102, 168-174. https://doi.org/10.1016/j.chaos.2017.04.029

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keywords = "Fractional-time derivative, Inverse subordinator, L{\'e}vy measure, Occupation measure, Subordinator",

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AU - Chen, Zhen Qing

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AB - 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.

KW - Fractional-time derivative

KW - Inverse subordinator

KW - Lévy measure

KW - Occupation measure

KW - Subordinator

UR - http://www.scopus.com/inward/record.url?scp=85018829215&partnerID=8YFLogxK

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DO - 10.1016/j.chaos.2017.04.029

M3 - Article

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VL - 102

SP - 168

EP - 174

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

ER -

Time fractional equations and probabilistic representation

Abstract

Keywords

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