Time fractional equations and probabilistic representation

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.

Minor revision in Section 4 "Note added after publication", to avoid using the closed graph theorem

References in corpus (2)

• Fractional Cauchy problems on bounded domains
• Mean exit time and escape probability for the anomalous processes with the tempered power-law waiting times

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