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

Fima C Klebaner; Anatolii Alfredovich Mogulskii

doi:10.33048/semi.2019.16.001

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

Fima C Klebaner, Anatolii Alfredovich Mogulskii

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-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 language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Siberian Electronic Mathematical Reports
Volume	16
DOIs	https://doi.org/10.33048/semi.2019.16.001
Publication status	Published - 2019

Keywords

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

Cite this

Klebaner, F. C., & Mogulskii, A. A. (2019). Large Deviations for processes on half-line: Random Walk and Compound Poisson. Siberian Electronic Mathematical Reports, 16, 1-20. https://doi.org/10.33048/semi.2019.16.001

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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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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 -

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10.33048/semi.2019.16.001

260314614-oaFinal published version, 194 KB

Projects

Measure-valued analysis of stochastic populations

Project: Research

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

Abstract

Keywords

Cite this

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Projects

Measure-valued analysis of stochastic populations