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

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

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 \mathnet{http://mi.mathnet.ru/msb2509} \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
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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
2. Rainer Dahlhaus, “ON THE ASYMPTOTIC DISTRIBUTION OF BARTLETT'S U<sub>p</sub>-STATISTIC”, J time ser anal, 6:4 (1985), 213
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
4. Gasanenko V., “Probability of the Wiener Process Stay in the Curvilinear Band”, no. 3, 1989, 5–6
5. Novikov A., Frishling V., Kordzakhia N., “Approximations of Boundary Crossing Probabilities for a Brownian Motion”, J. Appl. Probab., 36:4 (1999), 1019–1030
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
7. Li W., “The First Exit Time of a Brownian Motion From an Unbounded Convex Domain”, Ann. Probab., 31:2 (2003), 1078–1096
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
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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
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
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
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
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16. Frank Aurzada, Tanja Kramm, “The First Passage Time Problem Over a Moving Boundary for Asymptotically Stable Lévy Processes”, J Theor Probab, 2015
17. Dawei Lu, “Some asymptotic formulas for a Brownian motion from the maximum and minimum complicated domains”, Communications in Statistics - Theory and Methods, 2015
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