Properties of the deviation rate function and the asymptotics for the laplace transform of the distribution of a compound renewal process

Properties of the deviation rate function and the asymptotics for the laplace transform of the distribution of a compound renewal process Full article

Journal

Theory of Probability and its Applications
ISSN: 0040-585X , E-ISSN: 1095-7219

Output data

Year: 2020, Volume: 64, Number: 4, Pages: 499-512 Pages count : 14 DOI: 10.1137/S0040585X97T989660

Tags

Compound renewal process; Cramér’s condition; Deviation rate function; Laplace transform asymptotics; Large deviation principle; Large deviations; Legendre transform

Authors

Borovkov A.A. ¹ , Mogulskii A.A. ¹ , Prokopenko E.I. ¹

Affiliations

1	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation

We find the asymptotics for the logarithm of the Laplace transform of the distribution of a compound renewal process as time increases unboundedly. It is assumed that the elements of the governing sequences of the renewal process satisfy Cramér’s moment condition. Representations for the deviation rate function of the compound renewal process are found. © by SIAM.

Borovkov A.A. , Mogulskii A.A. , Prokopenko E.I.
Properties of the deviation rate function and the asymptotics for the laplace transform of the distribution of a compound renewal process
Theory of Probability and its Applications. 2020. V.64. N4. P.499-512. DOI: 10.1137/S0040585X97T989660 WOS Scopus OpenAlex

Боровков А.А. , Могульский А.А. , Прокопенко Е.И.
Свойства функции уклонений обобщенного процесса восстановления и асимптотика преобразования Лапласа над его распределением
Теория вероятностей и ее применения. 2019. Т.64. №4. С.625-641. DOI: 10.4213/tvp5285 OpenAlex

Web of science:	WOS:000551393100001
Scopus:	2-s2.0-85079616659
OpenAlex:	W3006514948

DB	Citing
Scopus	3
OpenAlex	2
Web of science	6