RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teor. Veroyatnost. i Primenen., 1964, Volume 9, Issue 3, Pages 498–515 (Mi tvp395)  

This article is cited in 4 scientific papers (total in 4 papers)

The Distribution of the First Jump

B. A. Rogozin

Novosibirsk

Abstract: The method of factorization [3], [4] is used for determining the distributions of the first positive value $\chi^ +$ and the maximum $\eta^+$ in the sequence $S_0=0$, $S_1$, $S_2$, …, $S_n=\sum\limits_{k=1}^n\xi_i$, $n\geqq 1$, where $\xi_1,\xi_2,…,\xi_n,…$ is a sequence of independent identically distributed random variables. The distribution of the first jump $\chi_x^+$ over a level $x>0$ and its limit as $x\to\infty$ are expressed in terms of the distribution of $\chi^+$. Formulas are given for evaluating these distributions by means of the distribution of $\xi_1$. The results presented supplement those in [8], [9] and [7].

Full text: PDF file (889 kB)

English version:
Theory of Probability and its Applications, 1964, 9:3, 450–465

Bibliographic databases:

Received: 20.01.1964

Citation: B. A. Rogozin, “The Distribution of the First Jump”, Teor. Veroyatnost. i Primenen., 9:3 (1964), 498–515; Theory Probab. Appl., 9:3 (1964), 450–465

Citation in format AMSBIB
\Bibitem{Rog64}
\by B.~A.~Rogozin
\paper The Distribution of the First Jump
\jour Teor. Veroyatnost. i Primenen.
\yr 1964
\vol 9
\issue 3
\pages 498--515
\mathnet{http://mi.mathnet.ru/tvp395}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=169298}
\zmath{https://zbmath.org/?q=an:0139.35501}
\transl
\jour Theory Probab. Appl.
\yr 1964
\vol 9
\issue 3
\pages 450--465
\crossref{https://doi.org/10.1137/1109060}


Linking options:
  • http://mi.mathnet.ru/eng/tvp395
  • http://mi.mathnet.ru/eng/tvp/v9/i3/p498

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. E. L. Presman, “Factorization methods and boundary problems for sums of random variables given on Markov chains”, Math. USSR-Izv., 3:4 (1969), 815–852  mathnet  crossref  mathscinet  zmath
    2. Sergey V. Nagaev, “Asymptotic formulas for probabilities of large deviations of ladder heights”, Theory Stoch. Process., 14(30):1 (2008), 100–116  mathnet  mathscinet  zmath
    3. R. Aliev, T. Khaniev, B. Gever, “Weak convergence theorem for ergodic distribution of stochastic process with a discrete interference of change and generalized reflecting barrier”, Theory Probab. Appl., 60:3 (2016), 502–513  mathnet  crossref  crossref  mathscinet  isi  elib
    4. R. T. Aliev, T. A. Khaniev, “On the Limiting Behavior of the Characteristic Function of the Ergodic Distribution of the Semi-Markov Walk with Two Boundaries”, Math. Notes, 102:4 (2017), 444–454  mathnet  crossref  crossref  mathscinet  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:194
    Full text:127

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020