Entrance laws at the origin of self-similar Markov processes in high dimensions
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- by Andreas E. Kyprianou, Victor Rivero, Batı Şengül and Ting Yang PDF
- Trans. Amer. Math. Soc. 373 (2020), 6227-6299 Request permission
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.References
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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
- 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). - © Copyright 2020 American Mathematical Society
- 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
- MathSciNet review: 4155177