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Transactions of the American Mathematical Society

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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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Additional Information

Andreas E. Kyprianou
Affiliation: Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom
MR Author ID: 615043
Email: a.kyprianou@bath.ac.uk

Victor Rivero
Affiliation: CIMAT A. C., Calle Jalisco s/n, Col. Valenciana, A. P. 402, C.P. 36000, Guanajuato, Gto., Mexico
MR Author ID: 709574
Email: rivero@cimat.mx

Batı Şengül
Affiliation: Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom
Email: batisengul@gmail.com

Ting Yang
Affiliation: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China; and Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China
Email: yangt@bit.edu.cn

DOI: https://doi.org/10.1090/tran/8086
Keywords: Self-similar Markov processes, Markov additive processes, entrance law, fluctuation theory.
Received by editor(s): December 28, 2018
Received by editor(s) in revised form: September 27, 2019, and December 19, 2019
Published electronically: July 3, 2020
Additional Notes: The research of the first author was supported by EPSRC grants EP/L002442/1 and EP/M001784/1.
The research of the second author was supported by EPSRC grants EP/M001784/1.
The research of the third author was supported by EPSRC grants EP/L002442/1.
The research of the fourth author was supported by EPSRC grants EP/L002442/1 and NSFC (grants No. 11501029 and 11731009).
Article copyright: © Copyright 2020 American Mathematical Society