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Teoriya Veroyatnostei i ee Primeneniya, 1957, Volume 2, Issue 1, Pages 126–135 (Mi tvp4964)  

This article is cited in 20 scientific papers (total in 21 papers)

Short Communications

On the Distribution of the First Positive Sum for a Sequence of Independent Random Variables

Ya. G. Sinai

Moscow
Received: 21.05.1956
English version:
Theory of Probability and its Applications, 1957, Volume 2, Issue 1, Pages 122–129
DOI: https://doi.org/10.1137/1102009
Document Type: Article
Language: Russian
Citation: Ya. G. Sinai, “On the Distribution of the First Positive Sum for a Sequence of Independent Random Variables”, Teor. Veroyatnost. i Primenen., 2:1 (1957), 126–135; Theory Probab. Appl., 2:1 (1957), 122–129
Citation in format AMSBIB
\Bibitem{Sin57}
\by Ya.~G.~Sinai
\paper On the Distribution of the First Positive Sum for a Sequence of Independent Random Variables
\jour Teor. Veroyatnost. i Primenen.
\yr 1957
\vol 2
\issue 1
\pages 126--135
\mathnet{http://mi.mathnet.ru/tvp4964}
\transl
\jour Theory Probab. Appl.
\yr 1957
\vol 2
\issue 1
\pages 122--129
\crossref{https://doi.org/10.1137/1102009}
Linking options:
  • https://www.mathnet.ru/eng/tvp4964
  • https://www.mathnet.ru/eng/tvp/v2/i1/p126
  • This publication is cited in the following 21 articles:
    1. 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
    2. 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
    3. 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
    4. 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
    5. Hui He, Jingning Liu, Mei Zhang, “On Seneta–Heyde scaling for a stable branching random walk”, Adv. Appl. Probab., 50:2 (2018), 565  crossref
    6. Francesco Caravenna, Loïc Chaumont, “An invariance principle for random walk bridges conditioned to stay positive”, Electron. J. Probab., 18:none (2013)  crossref
    7. Ya. G. Sinai, “Limit theorem for trigonometric sums. Theory of curlicues”, Russian Math. Surveys, 63:6 (2008), 1023–1029  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. N.H. Bingham, Handbook of Statistics, 19, Stochastic Processes: Theory and Methods, 2001, 171  crossref
    9. S. P. Novikov, L. A. Bunimovich, A. M. Vershik, B. M. Gurevich, E. I. Dinaburg, G. A. Margulis, V. I. Oseledets, S. A. Pirogov, K. M. Khanin, N. N. Chentsova, “Yakov Grigor'evich Sinai (on his sixtieth birthday)”, Russian Math. Surveys, 51:4 (1996), 765–778  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    10. R. A. Doney, P. E. Greenwood, “On the joint distribution of ladder variables of random walk”, Probab. Th. Rel. Fields, 94:4 (1993), 457  crossref
    11. P. Greenwood, E. Perkins, “Limit theorems for excursions from a moving boundary”, Theory Probab. Appl., 29:4 (1985), 731–743  mathnet  mathnet  crossref  isi
    12. P. Greenwood, E. Omey, J. L. Teugels, “Harmonic renewal measures”, Z. Wahrscheinlichkeitstheorie verw Gebiete, 59:3 (1982), 391  crossref
    13. P. Greenwood, E. Omey, J. L. Teugels, “Harmonic renewal measures and bivariate domains of attraction in fluctuation theory”, Z. Wahrscheinlichkeitstheorie verw Gebiete, 61:4 (1982), 527  crossref
    14. N. H. Bingham, “Maxima of sums of random variables and suprema of stable processes”, Z. Wahrscheinlichkeitstheorie verw Gebiete, 26:4 (1973), 273  crossref
    15. B. A. Rogozin, “The distribution of the first hit for stable and asymptotically stable walks on an interval”, Theory Probab. Appl., 17:2 (1973), 332–338  mathnet  mathnet  crossref
    16. B. A. Rogozin, “The distribution of the first ladder moment and height and fluctuations of random walk”, Theory Probab. Appl., 16:4 (1971), 575–595  mathnet  mathnet  crossref
    17. N. U. Prabhu, “Limit theorems for the single server queue with traffic intensity one”, Journal of Applied Probability, 7:1 (1970), 227  crossref
    18. N. U. Prabhu, “Limit theorems for the single server queue with traffic intensity one”, J. Appl. Probab., 7:01 (1970), 227  crossref
    19. V. I. Rotar', “On moments of the time and the value of the first jump over a curvilinear bound”, Theory Probab. Appl., 12:4 (1967), 690–695  mathnet  mathnet  crossref
    20. B. A. Rogozin, “On some classes of processes with independent increments”, Theory Probab. Appl., 10:3 (1965), 479–483  mathnet  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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