Strong Law of Large Numbers for a Function of the Local Times of a Transient Random Walk in Zd

Standard

Strong Law of Large Numbers for a Function of the Local Times of a Transient Random Walk in Z^d. / Asymont, Inna M.; Korshunov, Dmitry.

в: Journal of Theoretical Probability, Том 33, № 4, 01.12.2020, стр. 2315-2336.

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

Harvard

Asymont, IM & Korshunov, D 2020, 'Strong Law of Large Numbers for a Function of the Local Times of a Transient Random Walk in Z^d', Journal of Theoretical Probability, Том. 33, № 4, стр. 2315-2336. https://doi.org/10.1007/s10959-019-00937-6

APA

Asymont, I. M., & Korshunov, D. (2020). Strong Law of Large Numbers for a Function of the Local Times of a Transient Random Walk in Z^d. Journal of Theoretical Probability, 33(4), 2315-2336. https://doi.org/10.1007/s10959-019-00937-6

Vancouver

Asymont IM, Korshunov D. Strong Law of Large Numbers for a Function of the Local Times of a Transient Random Walk in Z^d. Journal of Theoretical Probability. 2020 дек. 1;33(4):2315-2336. doi: 10.1007/s10959-019-00937-6

Author

Asymont, Inna M. ; Korshunov, Dmitry. / Strong Law of Large Numbers for a Function of the Local Times of a Transient Random Walk in Z^d. в: Journal of Theoretical Probability. 2020 ; Том 33, № 4. стр. 2315-2336.

BibTeX

@article{055987bd0db64d3488ce4fbd08c398a7,

title = "Strong Law of Large Numbers for a Function of the Local Times of a Transient Random Walk in Zd",

abstract = "For an arbitrary transient random walk (Sn)n≥0 in Zd, d≥ 1 , we prove a strong law of large numbers for the spatial sum ∑x∈Zdf(l(n,x)) of a function f of the local times l(n,x)=∑i=0nI{Si=x}. Particular cases are the number of(a)visited sites [first considered by Dvoretzky and Erd{\H o}s (Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp 353–367, 1951)], which corresponds to the function f(i) = I{ i≥ 1 } ;(b)α-fold self-intersections of the random walk [studied by Becker and K{\"o}nig (J Theor Probab 22:365–374, 2009)], which corresponds to f(i) = iα;(c)sites visited by the random walk exactly j times [considered by Erd{\H o}s and Taylor (Acta Math Acad Sci Hung 11:137–162, 1960) and Pitt (Proc Am Math Soc 43:195–199, 1974)], where f(i) = I{ i= j}.",

keywords = "Local times, Strong law of large numbers, Transient random walk in Z, math><mml, Transient random walk in <mml, msup><mml, end{document}<inline-graphic xlink, usepackage{amssymb}, setlength{, usepackage{amsmath}, oddsidemargin}{-69pt}, math>, usepackage{wasysym}, usepackage{amsbsy}, begin{document}$${, usepackage{upgreek}, mi></mml, usepackage{amsfonts}, msup></mml, gif{"}, documentclass[12pt]{minimal}, href={"}10959_2019_937_Article_IEq12, mrow><mml, mi mathvariant={"}double-struck{"}>Z</mml, usepackage{mathrsfs}, mi>d</mml, mathbb {Z}}<^>d$$, >, MOMENTS",

author = "Asymont, {Inna M.} and Dmitry Korshunov",

year = "2020",

month = dec,

day = "1",

doi = "10.1007/s10959-019-00937-6",

language = "English",

volume = "33",

pages = "2315--2336",

journal = "Journal of Theoretical Probability",

issn = "0894-9840",

publisher = "Springer New York",

number = "4",

}

RIS

TY - JOUR

T1 - Strong Law of Large Numbers for a Function of the Local Times of a Transient Random Walk in Zd

AU - Asymont, Inna M.

AU - Korshunov, Dmitry

PY - 2020/12/1

Y1 - 2020/12/1

N2 - For an arbitrary transient random walk (Sn)n≥0 in Zd, d≥ 1 , we prove a strong law of large numbers for the spatial sum ∑x∈Zdf(l(n,x)) of a function f of the local times l(n,x)=∑i=0nI{Si=x}. Particular cases are the number of(a)visited sites [first considered by Dvoretzky and Erdős (Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp 353–367, 1951)], which corresponds to the function f(i) = I{ i≥ 1 } ;(b)α-fold self-intersections of the random walk [studied by Becker and König (J Theor Probab 22:365–374, 2009)], which corresponds to f(i) = iα;(c)sites visited by the random walk exactly j times [considered by Erdős and Taylor (Acta Math Acad Sci Hung 11:137–162, 1960) and Pitt (Proc Am Math Soc 43:195–199, 1974)], where f(i) = I{ i= j}.

AB - For an arbitrary transient random walk (Sn)n≥0 in Zd, d≥ 1 , we prove a strong law of large numbers for the spatial sum ∑x∈Zdf(l(n,x)) of a function f of the local times l(n,x)=∑i=0nI{Si=x}. Particular cases are the number of(a)visited sites [first considered by Dvoretzky and Erdős (Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp 353–367, 1951)], which corresponds to the function f(i) = I{ i≥ 1 } ;(b)α-fold self-intersections of the random walk [studied by Becker and König (J Theor Probab 22:365–374, 2009)], which corresponds to f(i) = iα;(c)sites visited by the random walk exactly j times [considered by Erdős and Taylor (Acta Math Acad Sci Hung 11:137–162, 1960) and Pitt (Proc Am Math Soc 43:195–199, 1974)], where f(i) = I{ i= j}.

KW - Local times

KW - Strong law of large numbers

KW - Transient random walk in Z

KW - math><mml

KW - Transient random walk in <mml

KW - msup><mml

KW - end{document}<inline-graphic xlink

KW - usepackage{amssymb}

KW - setlength{

KW - usepackage{amsmath}

KW - oddsidemargin}{-69pt}

KW - math>

KW - usepackage{wasysym}

KW - usepackage{amsbsy}

KW - begin{document}$${

KW - usepackage{upgreek}

KW - mi></mml

KW - usepackage{amsfonts}

KW - msup></mml

KW - gif"

KW - documentclass[12pt]{minimal}

KW - href="10959_2019_937_Article_IEq12

KW - mrow><mml

KW - mi mathvariant="double-struck">Z</mml

KW - usepackage{mathrsfs}

KW - mi>d</mml

KW - mathbb {Z}}<^>d$$

KW - >

KW - MOMENTS

UR - http://www.scopus.com/inward/record.url?scp=85072040979&partnerID=8YFLogxK

U2 - 10.1007/s10959-019-00937-6

DO - 10.1007/s10959-019-00937-6

M3 - Article

AN - SCOPUS:85072040979

VL - 33

SP - 2315

EP - 2336

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 4

ER -

ID: 27417390