REFLECTING LEVY PROCESSES AND ASSOCIATED FAMILIES OF LINEAR OPERATORS

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REFLECTING LEVY PROCESSES AND ASSOCIATED FAMILIES OF LINEAR OPERATORS. / Ibragimov, I. A.; Smorodina, N. V.; Faddeev, M. M.

в: Theory of Probability and its Applications, Том 64, № 3, 01.01.2019, стр. 335-354.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{c18e20660064455aac0f94d100e335cb,

title = "REFLECTING LEVY PROCESSES AND ASSOCIATED FAMILIES OF LINEAR OPERATORS",

abstract = "The paper is concerned with special one-dimensional Markov processes, which are L{\'e}vy processes defined on a finite interval and reflected from the boundary points of the interval. It is shown that in this setting, in addition to the standard semigroup of operators generated by the Markov process, there also appears the family of “boundary” random operators that send functions defined on the boundary of the interval to elements of the space L2 on the entire interval. In the case when the original process is a Wiener process, we show that these operators can be expressed in terms of the local time of the process on the boundary of the interval.",

keywords = "Initial boundary value problem, Limit theorem, Local time, Random process, random process, BOUNDARY VALUE-PROBLEMS, DOMAIN PROBABILISTIC REPRESENTATIONS, initial boundary value problem, limit theorem, local time",

author = "Ibragimov, {I. A.} and Smorodina, {N. V.} and Faddeev, {M. M.}",

year = "2019",

month = jan,

day = "1",

doi = "10.1137/S0040585X97T989532",

language = "English",

volume = "64",

pages = "335--354",

journal = "Theory of Probability and its Applications",

issn = "0040-585X",

publisher = "Society for Industrial and Applied Mathematics",

number = "3",

}

RIS

TY - JOUR

T1 - REFLECTING LEVY PROCESSES AND ASSOCIATED FAMILIES OF LINEAR OPERATORS

AU - Ibragimov, I. A.

AU - Smorodina, N. V.

AU - Faddeev, M. M.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The paper is concerned with special one-dimensional Markov processes, which are Lévy processes defined on a finite interval and reflected from the boundary points of the interval. It is shown that in this setting, in addition to the standard semigroup of operators generated by the Markov process, there also appears the family of “boundary” random operators that send functions defined on the boundary of the interval to elements of the space L2 on the entire interval. In the case when the original process is a Wiener process, we show that these operators can be expressed in terms of the local time of the process on the boundary of the interval.

AB - The paper is concerned with special one-dimensional Markov processes, which are Lévy processes defined on a finite interval and reflected from the boundary points of the interval. It is shown that in this setting, in addition to the standard semigroup of operators generated by the Markov process, there also appears the family of “boundary” random operators that send functions defined on the boundary of the interval to elements of the space L2 on the entire interval. In the case when the original process is a Wiener process, we show that these operators can be expressed in terms of the local time of the process on the boundary of the interval.

KW - Initial boundary value problem

KW - Limit theorem

KW - Local time

KW - Random process

KW - random process

KW - BOUNDARY VALUE-PROBLEMS

KW - DOMAIN PROBABILISTIC REPRESENTATIONS

KW - initial boundary value problem

KW - limit theorem

KW - local time

UR - http://www.scopus.com/inward/record.url?scp=85074335930&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97T989532

DO - 10.1137/S0040585X97T989532

M3 - Article

AN - SCOPUS:85074335930

VL - 64

SP - 335

EP - 354

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 3

ER -

ID: 48923776

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