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Mat. Sb. (N.S.), 1979, Volume 110(152), Number 4(12), Pages 539–550 (Mi msb2509)  

This article is cited in 17 scientific papers (total in 17 papers)

On estimates and the asymptotic behavior of nonexit probabilities of a Wiener process to a moving boundary

A. A. Novikov


Abstract: In this paper the asymptotic behavior, as well as upper and lower bounds, is found for the probabilities $\mathsf P\{\sigma>T\}=\mathsf P\{|w_t|\leqslant f(t),0\leqslant t\leqslant T\}$, $\mathsf P\{\sigma>T\}=\mathsf P\{w_t\geqslant g(t),0\leqslant t\leqslant T\}$ for large classes of functions $f$ and $g$.
Bibliography: 21 titles.

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English version:
Mathematics of the USSR-Sbornik, 1981, 38:4, 495–505

Bibliographic databases:

UDC: 519.2
MSC: 60J65
Received: 18.01.1979

Citation: A. A. Novikov, “On estimates and the asymptotic behavior of nonexit probabilities of a Wiener process to a moving boundary”, Mat. Sb. (N.S.), 110(152):4(12) (1979), 539–550; Math. USSR-Sb., 38:4 (1981), 495–505

Citation in format AMSBIB
\Bibitem{Nov79}
\by A.~A.~Novikov
\paper On estimates and the asymptotic behavior of nonexit probabilities of a~Wiener process to a~moving boundary
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 110(152)
\issue 4(12)
\pages 539--550
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=562208}
\zmath{https://zbmath.org/?q=an:0462.60079|0425.60066}
\transl
\jour Math. USSR-Sb.
\yr 1981
\vol 38
\issue 4
\pages 495--505
\crossref{https://doi.org/10.1070/SM1981v038n04ABEH001455}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981LQ11400004}


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    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. Arato M., “Round-Off Error Propagation in the Integration of Ordinary Differential-Equations by One-Step Methods”, 45, no. 1-4, 1983, 23–31  mathscinet  zmath  isi
    2. Rainer Dahlhaus, “ON THE ASYMPTOTIC DISTRIBUTION OF BARTLETT'S U<sub>p</sub>-STATISTIC”, J time ser anal, 6:4 (1985), 213  crossref  mathscinet  zmath
    3. Salminen P., “On the 1st Hitting Time and the Last Exit Time for a Brownian-Motion to From a Moving Boundary”, Adv. Appl. Probab., 20:2 (1988), 411–426  crossref  mathscinet  zmath  isi
    4. Gasanenko V., “Probability of the Wiener Process Stay in the Curvilinear Band”, no. 3, 1989, 5–6  mathscinet  isi
    5. Novikov A., Frishling V., Kordzakhia N., “Approximations of Boundary Crossing Probabilities for a Brownian Motion”, J. Appl. Probab., 36:4 (1999), 1019–1030  crossref  mathscinet  zmath  isi
    6. Grillo G., “Off-Diagonal Bounds of Non-Gaussian Type for the Dirichlet Heat Kernel”, J. Lond. Math. Soc.-Second Ser., 62:Part 2 (2000), 599–612  crossref  mathscinet  zmath  isi
    7. Li W., “The First Exit Time of a Brownian Motion From an Unbounded Convex Domain”, Ann. Probab., 31:2 (2003), 1078–1096  crossref  mathscinet  zmath  isi
    8. Bischoff W., Hashorva E., “A Lower Bound for Boundary Crossing Probabilities of Brownian Bridge/Motion with Trend”, Stat. Probab. Lett., 74:3 (2005), 265–271  crossref  mathscinet  zmath  isi
    9. Lixin Song, Dawei Lu, Jinghai Feng, “The first exit time for a Bessel process from the minimum and maximum random domains”, Statistics & Probability Letters, 79:20 (2009), 2115  crossref  mathscinet  zmath
    10. Dawei Lu, Lixin Song, “The First Exit Time of a Brownian Motion from the Minimum and Maximum Parabolic Domains”, J Theoret Probab, 2010  crossref  mathscinet
    11. Dawei Lu, Lixin Song, “The Asymptotic Behavior of a Brownian Motion with a Drift from a Random Domain”, Communications in Statistics - Theory and Methods, 41:1 (2012), 62  crossref  mathscinet  zmath
    12. Aurzada F., Dereich S., “Universality of the Asymptotics of the One-Sided Exit Problem for Integrated Processes”, Ann. Inst. Henri Poincare-Probab. Stat., 49:1 (2013), 236–251  crossref  mathscinet  zmath  adsnasa  isi
    13. Dawei Lu, Lixin Song, “Some Asymptotic Formulas for a Brownian Motion with a Regular Variation from a Parabolic Domain”, Communications in Statistics - Theory and Methods, 2013, 1304221333  crossref  mathscinet
    14. LIXIN SONG, WENBIN CHE, DAWEI LU, “THE EXIT PROBABILITIES OF BROWNIAN MOTION WITH VARIABLE DIMENSION APPLYING TO THE CONTROL OF POPULATION GROWTH”, Int. J. Biomath, 2013, 1350027  crossref  mathscinet  zmath
    15. Dawei Lu, “Some Asymptotic Formulas for a Brownian Motion from The Maximum and Minimum Domains with Regular Varying Boundary”, Communications in Statistics - Theory and Methods, 43:18 (2014), 3848  crossref  mathscinet  zmath
    16. Frank Aurzada, Tanja Kramm, “The First Passage Time Problem Over a Moving Boundary for Asymptotically Stable Lévy Processes”, J Theor Probab, 2015  crossref  mathscinet
    17. Dawei Lu, “Some asymptotic formulas for a Brownian motion from the maximum and minimum complicated domains”, Communications in Statistics - Theory and Methods, 2015  crossref  mathscinet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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