A. A. Borovkov, “On factorization identities and properties of the distribution of the sequential sums supremum”, Teor. Veroyatnost. i Primenen., 15:3 (1970), 377–418; Theory Probab. Appl., 15:2 (1970), 359

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Teoriya Veroyatnostei i ee Primeneniya, 1970, Volume 15, Issue 3, Pages 377–418 (Mi tvp1853)

This article is cited in 38 scientific papers (total in 38 papers)

On factorization identities and properties of the distribution of the sequential sums supremum

A. A. Borovkov

Novosibirsk

Full-text PDF (2030 kB) Citations (38)

Abstract: The paper consists of two parts. The first one is mostly of surveying character and in particular, treats analytical methods of obtaining multiparametrical factorization identities. These methods, being simple enough, seem to contain more possibilities in comparison with direct probabilistic approaches.
The second part treats the investigation of properties of the sequential sums supremum of independent identically distributed random variables.

Received: 23.10.1969

English version:
Theory of Probability and its Applications, 1970, Volume 15, Issue 2, Pages 359–402
DOI: https://doi.org/10.1137/1115046

Bibliographic databases:

Language: Russian

Citation: A. A. Borovkov, “On factorization identities and properties of the distribution of the sequential sums supremum”, Teor. Veroyatnost. i Primenen., 15:3 (1970), 377–418; Theory Probab. Appl., 15:2 (1970), 359–402

Citation in format AMSBIB

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\jour Theory Probab. Appl.

\yr 1970

\vol 15

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\pages 359--402

\crossref{https://doi.org/10.1137/1115046}

Linking options:

https://www.mathnet.ru/eng/tvp1853

https://www.mathnet.ru/eng/tvp/v15/i3/p377

This publication is cited in the following 38 articles:

Ion Grama, Hui Xiao, “Conditioned local limit theorems for random walks on the real line”, Ann. Inst. H. Poincaré Probab. Statist., 61:1 (2025)
Mihalis G. Markakis, Eytan Modiano, John N. Tsitsiklis, “Delay Analysis of the Max-Weight Policy Under Heavy-Tailed Traffic via Fluid Approximations”, Mathematics of OR, 43:2 (2018), 460
S. Zh. Aibatov, L. G. Afanasyeva, “Subexponential asymptotics for steady state tail probabilities in a single-server queue with regenerative input flow”, Theory Probab. Appl., 62:3 (2018), 339–355
Iosif Pinelis, “Characteristic function of the positive part of a random variable and related results, with applications”, Statistics & Probability Letters, 106 (2015), 281
V. I. Lotov, A. S. Tarasenko, “On the distribution of the first exit time and overshoot in a two-sided boundary crossing problem”, Siberian Adv. Math., 23:2 (2013), 91–98
A. E. Kuznetsov, “Analytical proof of Pecherskii–Rogozin identity and Wiener–Hopf factorization”, Theory Probab. Appl., 55:3 (2011), 432–443
A. A. Mogul'skii, “Local limit theorem for the first crossing time of a fixed level by a random walk”, Siberian Adv. Math., 20:3 (2010), 191–200
Onno Boxma, Bert Zwart, “Tails in scheduling”, SIGMETRICS Perform. Eval. Rev., 34:4 (2007), 13
A. A. Mogul'skii, B. A. Rogozin, “A Local Theorem for the First Hitting Time of a Fixed Level by a Random Walk”, Siberian Adv. Math., 15:3 (2005), 1–27
Yozo TAMURA, Hiroshi TANAKA, “On a Fluctuation Identity for Multidimensional Lévy Processes”, Tokyo J. Math., 25:2 (2002)
Ken-iti Sato, Lévy Processes, 2001, 3
Boris Tsybakov, Nicolas D. Georganas, “Self-similar traffic and upper bounds to buffer-overflow probability in an ATM queue”, Performance Evaluation, 32:1 (1998), 57
V. B. Nevzorov, “Distribution of the Maximal Term of Sample Mean Sequence”, Theory Probab. Appl., 32:1 (1987), 117–121
G. Hooghiemstra, “Conditioned limit theorems for waiting-time processes of the M/G/1 queue”, Journal of Applied Probability, 20:3 (1983), 675
G. Hooghiemstra, “Conditioned limit theorems for waiting-time processes of the M/G/1 queue”, J. Appl. Probab., 20:03 (1983), 675
Genji Yamazaki, “An ordering relation of the blocking two-stage tandem queueing system to the reduced single server queueing system”, Ann Inst Stat Math, 33:1 (1981), 115
V. I. Afanas'ev, “Conditioned stable random walk with a negative drift”, Theory Probab. Appl., 24:1 (1979), 192–199
L. E. N. Delbrouck, “Numerical approximations for compound geometric distributions with applications in queueing theory”, J. Appl. Probab., 15:01 (1978), 202
L. E. N. Delbrouck, “Numerical approximations for compound geometric distributions with applications in queueing theory”, Journal of Applied Probability, 15:1 (1978), 202
Khursheed Alam, “Asymptotic property of the distribution of the maxima of a random walk”, Stochastic Processes and their Applications, 7:3 (1978), 337

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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