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

Andreas Kyprianou; Victor Rivero Mercado; Bati Sengul; Ting Yang

doi:10.1090/tran/8086

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

Andreas Kyprianou, Victor Rivero Mercado, Bati Sengul, Ting Yang

Research output: Contribution to journal › Article › peer-review

7 Citations (SciVal)

71 Downloads (Pure)

Abstract

In this paper we consider the problem of finding entrance laws at the origin for self-similar Markov processes in 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
Pages (from-to)	6227-6299
Number of pages	57
Journal	Transactions of the American Mathematical Society
Volume	373
Issue number	9
Early online date	3 Jul 2020
DOIs	https://doi.org/10.1090/tran/8086
Publication status	Published - 30 Sept 2020

Access to Document

10.1090/tran/8086

TAMS(revised14).PDF
First published in Trans. Amer. Math. Soc. vol (date), published by the American Mathematical Society. © 2020 American Mathematical Society.
Accepted author manuscript, 676 KB

Cite this

@article{56c885bc3a0c4f969efafcb51cc8cc04,

title = "Entrance laws at the origin of self-similar Markov processes in high dimensions",

abstract = "In this paper we consider the problem of finding entrance laws at the origin for self-similar Markov processes in Rd, 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.",

author = "Andreas Kyprianou and {Rivero Mercado}, Victor and Bati Sengul and Ting Yang",

year = "2020",

month = sep,

day = "30",

doi = "10.1090/tran/8086",

language = "English",

volume = "373",

pages = "6227--6299",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "9",

}

TY - JOUR

T1 - Entrance laws at the origin of self-similar Markov processes in high dimensions

AU - Kyprianou, Andreas

AU - Rivero Mercado, Victor

AU - Sengul, Bati

AU - Yang, Ting

PY - 2020/9/30

Y1 - 2020/9/30

N2 - In this paper we consider the problem of finding entrance laws at the origin for self-similar Markov processes in Rd, 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.

AB - In this paper we consider the problem of finding entrance laws at the origin for self-similar Markov processes in Rd, 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.

UR - https://arxiv.org/pdf/1812.01926.pdf

U2 - 10.1090/tran/8086

DO - 10.1090/tran/8086

M3 - Article

SN - 0002-9947

VL - 373

SP - 6227

EP - 6299

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 9

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

Self Similarity and Stable Processes

Real-Valued Self-Similar Markov Processes and their Applications

Cite this

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

Abstract

Access to Document

Other files and links

Fingerprint

Projects

Self Similarity and Stable Processes

Real-Valued Self-Similar Markov Processes and their Applications

Cite this