Entrance laws at the origin of self-similar Markov processes in high dimensions

Kyprianou, Andreas; Rivero, Victor; Şengül, Batı; Yang, Ting

doi:10.1090/tran/8086

Entrance laws at the origin of self-similar Markov processes in high dimensions

Authors: Andreas E. Kyprianou, Victor Rivero, Batı Şengül and Ting Yang
Journal: Trans. Amer. Math. Soc. 373 (2020), 6227-6299
MSC (2010): Primary 60G18, 60G51; Secondary 60B10, 60J45
DOI: https://doi.org/10.1090/tran/8086
Published electronically: July 3, 2020
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Abstract: In this paper we consider the problem of finding entrance laws at the origin for self-similar Markov processes in $\mathbb{R}^d$ , killed upon hitting the origin. Under suitable assumptions, we show the existence of an entrance law and the convergence to this law when the process is started close to the origin. We obtain an explicit description of the process started from the origin as the time reversal of the original self-similar Markov process conditioned to hit the origin.

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