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Teoriya Veroyatnostei i ee Primeneniya, 1971, Volume 16, Issue 4, Pages 593–613 (Mi tvp2321)  

This article is cited in 73 scientific papers (total in 73 papers)

The distribution of the first ladder moment and height and fluctuations of random walk

B. A. Rogozin

Novosibirsk
Abstract: Let ξ1,ξ2, be independent identically destributed random variables, and let S0=0, Sn=ni=1ξi, T=min{n:Sn>0}, H=ST.
In the paper, the distributions of T and H are investigated.
Received: 13.04.1970
English version:
Theory of Probability and its Applications, 1971, Volume 16, Issue 4, Pages 575–595
DOI: https://doi.org/10.1137/1116067
Bibliographic databases:
Language: Russian
Citation: B. A. Rogozin, “The distribution of the first ladder moment and height and fluctuations of random walk”, Teor. Veroyatnost. i Primenen., 16:4 (1971), 593–613; Theory Probab. Appl., 16:4 (1971), 575–595
Citation in format AMSBIB
\Bibitem{Rog71}
\by B.~A.~Rogozin
\paper The distribution of the first ladder moment and height and fluctuations of random walk
\jour Teor. Veroyatnost. i Primenen.
\yr 1971
\vol 16
\issue 4
\pages 593--613
\mathnet{http://mi.mathnet.ru/tvp2321}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=290473}
\zmath{https://zbmath.org/?q=an:0269.60053}
\transl
\jour Theory Probab. Appl.
\yr 1971
\vol 16
\issue 4
\pages 575--595
\crossref{https://doi.org/10.1137/1116067}
Linking options:
  • https://www.mathnet.ru/eng/tvp2321
  • https://www.mathnet.ru/eng/tvp/v16/i4/p593
  • This publication is cited in the following 73 articles:
    1. Stergios B. Fotopoulos, “The distribution of the maximum likelihood estimates of the change point and their relation to random walks”, Stat Inference Stoch Process, 27:2 (2024), 335  crossref
    2. V. A. Vatutin, E. E. Dyakonova, “On the prospective minimum of the random walk conditioned to stay nonnegative”, Discrete Math. Appl., 34:6 (2024), 337–362  mathnet  crossref  crossref  isi
    3. Wenming Hong, Mingyang Sun, “First-passage time for Sinai's random walk in a random environment”, J. Appl. Probab., 2024, 1  crossref
    4. V. A. Vatutin, C. Dong, E. E. Dyakonova, “Some functionals for random walks and critical branching processes in an extremely unfavourable random environment”, Sb. Math., 215:10 (2024), 1321–1350  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    5. V. A. Vatutin, E. E. Dyakonova, “Population size of a critical branching process evolving in unfovarable environment”, Theory Probab. Appl., 68:3 (2023), 411–430  mathnet  crossref  crossref  mathscinet
    6. V. A. Vatutin, C. Dong, E. E. Dyakonova, “Random walks conditioned to stay nonnegative and branching processes in an unfavourable environment”, Sb. Math., 214:11 (2023), 1501–1533  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. V. I. Lotov, “O svoistvakh granichnykh funktsionalov dlya sluchainogo bluzhdaniya s ustoichivymi raspredeleniyami skachkov”, Sib. elektron. matem. izv., 20:1 (2023), 455–464  mathnet  crossref
    8. Denis Denisov, Vitali Wachtel, “Green Function for an Asymptotically Stable Random Walk in a Half Space”, J Theor Probab, 2023  crossref
    9. Micha Buck, “Limit Theorems for Random Walks with Absorption”, J Theor Probab, 34:1 (2021), 241  crossref
    10. Dyakonova E. Li D. Vatutin V. Zhang M., “Branching Processes in a Random Environment With Immigration Stopped At Zero”, J. Appl. Probab., 57:1 (2020), PII S0021900219000949, 237–249  crossref  isi
    11. Kohei Uchiyama, “The potential function and ladder heights of a recurrent random walk on Z with infinite variance”, Electron. J. Probab., 25:none (2020)  crossref
    12. Kôhei Uchiyama, “A renewal theorem for relatively stable variables”, Bull. London Math. Soc., 52:6 (2020), 1174  crossref
    13. Aleksandar Mijatović, Vladislav Vysotsky, “Stability of overshoots of zero mean random walks”, Electron. J. Probab., 25:none (2020)  crossref
    14. Eugene Seneta, “Slowly varying functions in the Zygmund sense and generalized regular variation”, Journal of Mathematical Analysis and Applications, 475:2 (2019), 1647  crossref
    15. Quentin Berger, “Notes on random walks in the Cauchy domain of attraction”, Probab. Theory Relat. Fields, 175:1-2 (2019), 1  crossref
    16. Kôhei Uchiyama, “Asymptotically stable random walks of index 1<α<2 killed on a finite set”, Stochastic Processes and their Applications, 129:12 (2019), 5151  crossref
    17. Igor Kortchemski, Loïc Richier, “Condensation in critical Cauchy Bienaymé–Galton–Watson trees”, Ann. Appl. Probab., 29:3 (2019)  crossref
    18. Hui He, Jingning Liu, Mei Zhang, “On Seneta–Heyde scaling for a stable branching random walk”, Adv. Appl. Probab., 50:2 (2018), 565  crossref
    19. Eugene Seneta, “The weak law of large numbers for nonnegative summands”, Adv. Appl. Probab., 50:A (2018), 241  crossref
    20. M.M. Osypchuk, M.I. Portenko, “On the distribution of a rotationally invariant α-stable process at the hitting time of a given hyperplane”, Dopov. Nac. akad. nauk Ukr., 2018, no. 12, 14  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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