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Abstract: A Brownian time process is a Markov process subordinated to the absolutevalue of an independent one-dimensional Brownian motion. Its transitiondensities solve an initial value problem involving the square of the generatorof the original Markov process. An apparently unrelated class of processes,emerging as the scaling limits of continuous time random walks, involvesubordination to the inverse or hitting time process of a classical stablesubordinator. The resulting densities solve fractional Cauchy problems, anextension that involves fractional derivatives in time. In this paper, we willshow a close and unexpected connection between these two classes of processes,and consequently, an equivalence between these two families of partialdifferential equations.



Autor: Boris Baeumer, Mark M. Meerschaert, Erkan Nane

Fuente: https://arxiv.org/







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