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Large deviation principle for multidimensional first compound renewal processes in the phase space. / Mogulskii, Anatolii Alfredovich; Prokopenko, Evgenii Igorevich.

In: Сибирские электронные математические известия, Vol. 16, 101, 01.11.2019, p. 1464-1477.

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

Harvard

Mogulskii, AA & Prokopenko, EI 2019, 'Large deviation principle for multidimensional first compound renewal processes in the phase space', Сибирские электронные математические известия, vol. 16, 101, pp. 1464-1477. https://doi.org/10.33048/SEMI.2019.16.101

APA

Mogulskii, A. A., & Prokopenko, E. I. (2019). Large deviation principle for multidimensional first compound renewal processes in the phase space. Сибирские электронные математические известия, 16, 1464-1477. [101]. https://doi.org/10.33048/SEMI.2019.16.101

Vancouver

Mogulskii AA, Prokopenko EI. Large deviation principle for multidimensional first compound renewal processes in the phase space. Сибирские электронные математические известия. 2019 Nov 1;16:1464-1477. 101. doi: 10.33048/SEMI.2019.16.101

Author

Mogulskii, Anatolii Alfredovich ; Prokopenko, Evgenii Igorevich. / Large deviation principle for multidimensional first compound renewal processes in the phase space. In: Сибирские электронные математические известия. 2019 ; Vol. 16. pp. 1464-1477.

BibTeX

@article{9892ac5d0299457f8fdb939491fc633d,
title = "Large deviation principle for multidimensional first compound renewal processes in the phase space",
abstract = "We obtain the large deviation principles for multidimensional first compound renewal processes Z(t) in the phase space Rd, for this we find and investigate the rate function DZ(α). Also we find asymptotics for the Laplace transform of this process when the time goes to infinity, for this we find and investigate the so-called fundamental function AZ(μ).",
keywords = "Compound multidimensional renewal process, Cramer's condition, Deviation (rate) function, Fundamental function, Large deviations, Renewal measure, Second deviation (rate) function, large deviations, INTEGRO-LOCAL THEOREMS, compound multidimensional renewal process, fundamental function, second deviation (rate) function, renewal measure, deviation (rate) function",
author = "Mogulskii, {Anatolii Alfredovich} and Prokopenko, {Evgenii Igorevich}",
year = "2019",
month = nov,
day = "1",
doi = "10.33048/SEMI.2019.16.101",
language = "English",
volume = "16",
pages = "1464--1477",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - Large deviation principle for multidimensional first compound renewal processes in the phase space

AU - Mogulskii, Anatolii Alfredovich

AU - Prokopenko, Evgenii Igorevich

PY - 2019/11/1

Y1 - 2019/11/1

N2 - We obtain the large deviation principles for multidimensional first compound renewal processes Z(t) in the phase space Rd, for this we find and investigate the rate function DZ(α). Also we find asymptotics for the Laplace transform of this process when the time goes to infinity, for this we find and investigate the so-called fundamental function AZ(μ).

AB - We obtain the large deviation principles for multidimensional first compound renewal processes Z(t) in the phase space Rd, for this we find and investigate the rate function DZ(α). Also we find asymptotics for the Laplace transform of this process when the time goes to infinity, for this we find and investigate the so-called fundamental function AZ(μ).

KW - Compound multidimensional renewal process

KW - Cramer's condition

KW - Deviation (rate) function

KW - Fundamental function

KW - Large deviations

KW - Renewal measure

KW - Second deviation (rate) function

KW - large deviations

KW - INTEGRO-LOCAL THEOREMS

KW - compound multidimensional renewal process

KW - fundamental function

KW - second deviation (rate) function

KW - renewal measure

KW - deviation (rate) function

UR - http://www.scopus.com/inward/record.url?scp=85083236685&partnerID=8YFLogxK

U2 - 10.33048/SEMI.2019.16.101

DO - 10.33048/SEMI.2019.16.101

M3 - Article

AN - SCOPUS:85083236685

VL - 16

SP - 1464

EP - 1477

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

M1 - 101

ER -

ID: 24068158