Large Deviations for processes on half-line: Random Walk and Compound Poisson

Fima C Klebaner, Anatolii Alfredovich Mogulskii

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We establish, under the Cramer exponential moment condition in a neighbourhood of zero, the Extended Large Deviation Principle for the Random Walk and the Compound Poisson processes in the metric space V of functions of finite variation on [0;1) with the modified Borovkov metric.
Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalSiberian Electronic Mathematical Reports
Volume16
DOIs
Publication statusPublished - 2019

Keywords

  • Large Deviations
  • Random Walk
  • Compound Poisson Process
  • Cramer’s condition
  • rate function
  • Extended Large Deviation Principle

Cite this

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title = "Large Deviations for processes on half-line: Random Walk and Compound Poisson",
abstract = "We establish, under the Cramer exponential moment condition in a neighbourhood of zero, the Extended Large Deviation Principle for the Random Walk and the Compound Poisson processes in the metric space V of functions of finite variation on [0;1) with the modified Borovkov metric.",
keywords = "Large Deviations, Random Walk, Compound Poisson Process, Cramer’s condition, rate function, Extended Large Deviation Principle",
author = "Klebaner, {Fima C} and Mogulskii, {Anatolii Alfredovich}",
year = "2019",
doi = "10.33048/semi.2019.16.001",
language = "English",
volume = "16",
pages = "1--20",
journal = "Siberian Electronic Mathematical Reports",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

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Large Deviations for processes on half-line : Random Walk and Compound Poisson. / Klebaner, Fima C; Mogulskii, Anatolii Alfredovich.

In: Siberian Electronic Mathematical Reports, Vol. 16, 2019, p. 1-20.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Large Deviations for processes on half-line

T2 - Random Walk and Compound Poisson

AU - Klebaner, Fima C

AU - Mogulskii, Anatolii Alfredovich

PY - 2019

Y1 - 2019

N2 - We establish, under the Cramer exponential moment condition in a neighbourhood of zero, the Extended Large Deviation Principle for the Random Walk and the Compound Poisson processes in the metric space V of functions of finite variation on [0;1) with the modified Borovkov metric.

AB - We establish, under the Cramer exponential moment condition in a neighbourhood of zero, the Extended Large Deviation Principle for the Random Walk and the Compound Poisson processes in the metric space V of functions of finite variation on [0;1) with the modified Borovkov metric.

KW - Large Deviations

KW - Random Walk

KW - Compound Poisson Process

KW - Cramer’s condition

KW - rate function

KW - Extended Large Deviation Principle

U2 - 10.33048/semi.2019.16.001

DO - 10.33048/semi.2019.16.001

M3 - Article

VL - 16

SP - 1

EP - 20

JO - Siberian Electronic Mathematical Reports

JF - Siberian Electronic Mathematical Reports

SN - 1813-3304

ER -