Локальные теоремы для конечномерных приращений арифметических многомерных обобщенных процессов восстановления при выполнении условия Крамера

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Локальные теоремы для конечномерных приращений арифметических многомерных обобщенных процессов восстановления при выполнении условия Крамера. / Logachov, Artem Vasilhevich; Mogulskii, Anatolii Alfredovich.

In: Сибирские электронные математические известия, Vol. 17, 2020, p. 1766-1786.

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

BibTeX

@article{9cc31f50e79e4ba88c6a5cc091f37f29,

title = "Локальные теоремы для конечномерных приращений арифметических многомерных обобщенных процессов восстановления при выполнении условия Крамера",

abstract = "We continue to study the compound renewal processes under the Cramer moment condition, which was started by A.A. Borovkov and A.A. Mogulskii (2013). In the present paper we study arithmetic multidimensional compound renewal process, for which the {"}controlling{"} random vector xi = (tau, zeta) (tau > 0 determines the distance between the jumps, zeta determines the value of jumps of the compound renewal process) has an arithmetic distribution with light tails. For these processes we propose wide conditions (close to necessary), under which we can find exact asymptotics in local limit theorems for finite - dimensional increments.",

keywords = "compound multidimensional arithmetic renewal process, large deviations, moderate deviations, renewal measure, Cramer's condition, rate function, local theorems for finite - dimensional increments, LARGE DEVIATION PRINCIPLES, DISTRIBUTIONS, TRAJECTORIES, BOUNDARY",

author = "Logachov, {Artem Vasilhevich} and Mogulskii, {Anatolii Alfredovich}",

year = "2020",

doi = "10.33048/semi.2020.17.120",

language = "русский",

volume = "17",

pages = "1766--1786",

journal = "Сибирские электронные математические известия",

issn = "1813-3304",

publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - Локальные теоремы для конечномерных приращений арифметических многомерных обобщенных процессов восстановления при выполнении условия Крамера

AU - Logachov, Artem Vasilhevich

AU - Mogulskii, Anatolii Alfredovich

PY - 2020

Y1 - 2020

N2 - We continue to study the compound renewal processes under the Cramer moment condition, which was started by A.A. Borovkov and A.A. Mogulskii (2013). In the present paper we study arithmetic multidimensional compound renewal process, for which the "controlling" random vector xi = (tau, zeta) (tau > 0 determines the distance between the jumps, zeta determines the value of jumps of the compound renewal process) has an arithmetic distribution with light tails. For these processes we propose wide conditions (close to necessary), under which we can find exact asymptotics in local limit theorems for finite - dimensional increments.

AB - We continue to study the compound renewal processes under the Cramer moment condition, which was started by A.A. Borovkov and A.A. Mogulskii (2013). In the present paper we study arithmetic multidimensional compound renewal process, for which the "controlling" random vector xi = (tau, zeta) (tau > 0 determines the distance between the jumps, zeta determines the value of jumps of the compound renewal process) has an arithmetic distribution with light tails. For these processes we propose wide conditions (close to necessary), under which we can find exact asymptotics in local limit theorems for finite - dimensional increments.

KW - compound multidimensional arithmetic renewal process

KW - large deviations

KW - moderate deviations

KW - renewal measure

KW - Cramer's condition

KW - rate function

KW - local theorems for finite - dimensional increments

KW - LARGE DEVIATION PRINCIPLES

KW - DISTRIBUTIONS

KW - TRAJECTORIES

KW - BOUNDARY

U2 - 10.33048/semi.2020.17.120

DO - 10.33048/semi.2020.17.120

M3 - статья

VL - 17

SP - 1766

EP - 1786

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 26076714