### 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.

$\mathbb{R}^d$,

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.

Original language | English |
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Number of pages | 57 |

Journal | Transactions of the American Mathematical Society |

Publication status | Published - 2019 |

### Cite this

Kyprianou, A., Rivero Mercado, V., Sengul, B., & Yang, T. (2019). Entrance laws at the origin of self-similar Markov processes in high dimensions.

*Transactions of the American Mathematical Society*.