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

Andreas E. Kyprianou; Victor Rivero; Bati Şengül; Ting Yang

doi:10.1090/tran/8086

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

Andreas E. Kyprianou, Victor Rivero, Bati Şengül, Ting Yang

School of Mathematics and Statistics

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

6 Citations (Scopus)

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	73
Journal	Transactions of the American Mathematical Society
Volume	373
Issue number	9
DOIs	https://doi.org/10.1090/tran/8086
Publication status	Published - Sept 2020

Keywords

Entrance law
Fluctuation theory
Markov additive processes
Self-similar Markov processes

Access to Document

10.1090/tran/8086

Cite this

@article{84c6a26111e04e6aa2376cbc7a2989cc,

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.",

keywords = "Entrance law, Fluctuation theory, Markov additive processes, Self-similar Markov processes",

author = "Kyprianou, {Andreas E.} and Victor Rivero and Bati {\c S}eng{\"u}l and Ting Yang",

note = "Publisher Copyright: {\textcopyright} 2020 American Mathematical Society",

year = "2020",

month = sep,

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 E.

AU - Rivero, Victor

AU - Şengül, Bati

AU - Yang, Ting

PY - 2020/9

Y1 - 2020/9

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.

KW - Entrance law

KW - Fluctuation theory

KW - Markov additive processes

KW - Self-similar Markov processes

UR - http://www.scopus.com/inward/record.url?scp=85092289428&partnerID=8YFLogxK

U2 - 10.1090/tran/8086

DO - 10.1090/tran/8086

M3 - Article

AN - SCOPUS:85092289428

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

Keywords

Access to Document

Other files and links

Fingerprint

Cite this