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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 298, Pages 5–21 (Mi znsl1148)  

This article is cited in 25 scientific papers (total in 25 papers)

Exact small ball constants for some Gaussian processes under L2-norm

L. Beghina, Ya. Yu. Nikitinb, E. Orsinghera

a Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma la Sapienza
b St. Petersburg State University, Department of Mathematics and Mechanics
References:
Abstract: We find some logarithmic and exact small deviation asymptotics for the L2-norm of certain Gaussian processes closely connected with the Wiener process. In particular the processes obtained by centering and integrating Brownian motion and Brownian bridge are examined.
Received: 12.10.2003
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 128, Issue 1, Pages 2493–2502
DOI: https://doi.org/10.1007/s10958-005-0197-9
Bibliographic databases:
UDC: 519.21
Language: English
Citation: L. Beghin, Ya. Yu. Nikitin, E. Orsingher, “Exact small ball constants for some Gaussian processes under L2-norm”, Probability and statistics. Part 6, Zap. Nauchn. Sem. POMI, 298, POMI, St. Petersburg, 2003, 5–21; J. Math. Sci. (N. Y.), 128:1 (2005), 2493–2502
Citation in format AMSBIB
\Bibitem{BegNikOrs03}
\by L.~Beghin, Ya.~Yu.~Nikitin, E.~Orsingher
\paper Exact small ball constants for some Gaussian processes under $L^2$-norm
\inbook Probability and statistics. Part~6
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 298
\pages 5--21
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1148}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2038861}
\zmath{https://zbmath.org/?q=an:1078.60028}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 128
\issue 1
\pages 2493--2502
\crossref{https://doi.org/10.1007/s10958-005-0197-9}
Linking options:
  • https://www.mathnet.ru/eng/znsl1148
  • https://www.mathnet.ru/eng/znsl/v298/p5
  • This publication is cited in the following 25 articles:
    1. L. V. Rozovskii, “Small deviation probabilities for sums of independent positive random variables”, Vestn. St. Petersbg. Univ., Math., 7:3 (2020), 295–307  mathnet  mathnet  crossref  crossref
    2. A.A. Khartov, M. Zani, “Approximation complexity of sums of random processes”, Journal of Complexity, 54 (2019), 101399  crossref
    3. V. R. Fatalov, “Integrals of Bessel processes and multi-dimensional Ornstein–Uhlenbeck processes: exact asymptotics for Lp-functionals”, Izv. Math., 82:2 (2018), 377–406  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Nazarov A.I., Nikitin Ya.Yu., “On Small Deviation Asymptotics in l-2 of Some Mixed Gaussian Processes”, 6, no. 4, 2018, 55  crossref  zmath  isi  scopus
    5. Ibragimov I.A., Lifshits M.A., Nazarov A.I., Zaporozhets D.N., “On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent Variables”, Vestn. St Petersb. Univ.-Math., 51:3 (2018), 213–236  crossref  mathscinet  isi  scopus
    6. Xiaohui Ai, Yang Sun, “Karhunen–Loeve expansion for the additive two-sided Brownian motion”, Communications in Statistics - Theory and Methods, 47:13 (2018), 3085  crossref
    7. Yu. P. Petrova, “Spectral Asymptotics for Problems with Integral Constraints”, Math. Notes, 102:3 (2017), 369–377  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Xiaohui Ai, “Karhunen–Loeve expansion for the additive detrended Brownian motion”, Communications in Statistics - Theory and Methods, 46:16 (2017), 8210  crossref
    9. Xiaohui Ai, “A note on Karhunen–Loève expansions for the demeaned stationary Ornstein–Uhlenbeck process”, Statistics & Probability Letters, 117 (2016), 113  crossref
    10. Kirichenko A.A., Nikitin Ya.Yu., “Precise Small Deviations in l-2 of Some Gaussian Processes Appearing in the Regression Context”, Cent. Eur. J. Math., 12:11 (2014), 1674–1686  crossref  mathscinet  zmath  isi  elib  scopus
    11. Ai XiaoHui, Li V W., “Karhunen-Loeve Expansions for the M-Th Order Detrended Brownian Motion”, Sci. China-Math., 57:10 (2014), 2043–2052  crossref  mathscinet  zmath  isi  scopus
    12. Liu J.V., Huang Z., Mao H., “Karhunen-Loeve Expansion for Additive Slepian Processes”, Stat. Probab. Lett., 90 (2014), 93–99  crossref  mathscinet  zmath  isi  elib  scopus
    13. V. R. Fatalov, “Ergodic means for large values of T and exact asymptotics of small deviations for a multi-dimensional Wiener process”, Izv. Math., 77:6 (2013), 1224–1259  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. Liu J.V., “Karhunen-Loeve Expansion for Additive Brownian Motions”, Stoch. Process. Their Appl., 123:11 (2013), 4090–4110  crossref  mathscinet  zmath  isi  elib  scopus
    15. Ya. Yu. Nikitin, R. S. Pusev, “The exact asymptotic of small deviations for a series of Brownian functionals”, Theory Probab. Appl., 57:1 (2013), 60–81  mathnet  crossref  crossref  zmath  isi  elib  elib
    16. Ai X., Li W.V., Liu G., “Karhunen-Loeve Expansions for the Detrended Brownian Motion”, Stat. Probab. Lett., 82:7 (2012), 1235–1241  crossref  mathscinet  zmath  isi  elib  scopus
    17. Mikhail Lifshits, SpringerBriefs in Mathematics, Lectures on Gaussian Processes, 2012, 1  crossref
    18. R. S. Pusev, “Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm”, Theoret. and Math. Phys., 165:1 (2010), 1348–1357  mathnet  crossref  crossref  adsnasa  isi
    19. A. I. Nazarov, “On one transformations family of Gaussian random functions”, Theory Probab. Appl., 54:2 (2010), 203–216  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. N. A. Serdyukova, “Dependence of the approximation complexity of random fields on dimension”, Theory Probab. Appl., 54:2 (2010), 272–284  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
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