Functional limit theorems for processes pieced together from excursions

2013/09/10 by Kouji Yano, Yano, Kouji
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1309.2652

arxiv created 2014/07/11 · arxiv updated 2014/07/14

Abstract

A notion of convergence of excursion measures is introduced. It is proved that convergence of excursion measures implies convergence in law of the processes pieced together from excursions. This result is applied to obtain homogenization theorems of jumping-in extensions for positive self-similar Markov processes, for Walsh diffusions and for the Brownian motion on the Sierpiński gasket.

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