Anscombe-type theorem and moderate deviations for trajectories of a compound renewal process

Logachov, A. V.; Mogulskii, A. A.

doi:10.1007/s10958-018-3661-z

Cited by 6 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…2 P r o o f of statement 5). From Consequence 3.2 (see [21]) it is follows that the sequence of random variables Z(n…”

Section: (Local Theorem In Regions Of Normal Moderate and Large Devia...mentioning

confidence: 99%

Limit theorems for chains with unbounded variable length memory which satisfy Cramer condition

2022

View full text Add to dashboard Cite

show abstract

“…2 P r o o f of statement 5). From Consequence 3.2 (see [21]) it is follows that the sequence of random variables Z(n…”

Section: (Local Theorem In Regions Of Normal Moderate and Large Devia...mentioning

confidence: 99%

Limit theorems for chains with unbounded variable length memory which satisfy Cramer condition

2022

View full text Add to dashboard Cite

show abstract

“…✷ P r o o f of statement 5). From Consequence 3.2 (see [10]) it is follows that the sequence of random variables Z(n…”

Section: (Local Theorem In Regions Of Normal Moderate and Large Devia...mentioning

confidence: 99%

Limit theorems for chains with unbounded variable length memory which satisfy Cramer condition

Logachev¹,

Mogulskii²,

Yambartsev³

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…There are many results on the theory of deviations for renewal processes or renewal reward processes. See, for example, Serfozo [18], Glynn and Whitt [8], Jiang [11], Chi [4], Lefevere et al [15], Borovkov and Mogulskii [1], Tsirelson [21], Logachov and Mogulskii [16], and the references therein. However, these proposed approaches cannot be applied directly to our case, since most of them require constraints on moments or moment generating functions for inter-occurrence times, which are not fulfilled by A n in our situations.…”

Section: Introductionmentioning

confidence: 99%

Large and moderate deviations for record numbers in some non–nearest neighbor random walks

Yao

2022

Electron. Commun. Probab.

View full text Add to dashboard Cite

The deviation principles of record numbers in random walk models have not been completely investigated, especially for the non-nearest neighbor cases. In this paper, we derive the asymptotic probabilities of large and moderate deviations for the number of "weak records" (or "ladder points") in two kinds of one-dimensional non-nearest neighbor random walks. The proofs depend only on the direct analysis of random walks. We illustrate that the traditional method of analyzing the local time of Brownian motions, which is often adopted for the simple random walks, would lead to wrong conjectures for our cases.

show abstract

Anscombe-type theorem and moderate deviations for trajectories of a compound renewal process

Cited by 6 publications

References 12 publications

Limit theorems for chains with unbounded variable length memory which satisfy Cramer condition

Limit theorems for chains with unbounded variable length memory which satisfy Cramer condition

Limit theorems for chains with unbounded variable length memory which satisfy Cramer condition

Large and moderate deviations for record numbers in some non–nearest neighbor random walks

Contact Info

Product

Resources

About