Modulus of continuity of a class of monofractal processes

2012/11/13 by Decrouez, Geoffrey, Hambly, Ben, Jones, Owen Dafydd
#28A80 #60G18 #60J85 #68U20 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1211.2895

Abstract

We derive the modulus of continuity of a class of processes called Canonical Embedded Branching Processes (CEBP), recently introduced by Decrouez and Jones, and we establish their monofractal character. CEBP provide a rich class of processes, including the Brownian motion as a particular case. The techniques developed in this study follow the steps of Barlow and Perkins on Brownian motion on a Sierpinski gasket, though complications arise here since CEBP are not Markovian in general.

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