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Uspekhi Mat. Nauk, 1997, Volume 52, Issue 2(314), Pages 119–138 (Mi umn822)  

This article is cited in 18 scientific papers (total in 18 papers)


Scientific papers in honour of R. L. Dobrushin
Distribution of the maximum of a fractional Brownian motion

Ya. G. Sinaiab

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Princeton University, Department of Mathematics

DOI: https://doi.org/10.4213/rm822

Full text: PDF file (294 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1997, 52:2, 359–378

Bibliographic databases:

UDC: 519.2
MSC: 60J65, 60E05, 60G15
Received: 15.09.1996

Citation: Ya. G. Sinai, “Distribution of the maximum of a fractional Brownian motion”, Uspekhi Mat. Nauk, 52:2(314) (1997), 119–138; Russian Math. Surveys, 52:2 (1997), 359–378

Citation in format AMSBIB
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\pages 119--138
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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. Molchan, GM, “On the maximum of a fractional Brownian motion”, Theory of Probability and Its Applications, 44:1 (1999), 97  crossref  mathscinet  zmath  isi
    2. Molchan, GM, “Maximum of a fractional Brownian motion: Probabilities of small values”, Communications in Mathematical Physics, 205:1 (1999), 97  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    3. Ruzmaikina, AA, “Stieltjes integrals of Holder continuous functions with applications to fractional Brownian motion”, Journal of Statistical Physics, 100:5–6 (2000), 1049  crossref  mathscinet  zmath  isi  elib
    4. Anh, VV, “Models for fractional Riesz-Bessel motion and related processes”, Fractals-Complex Geometry Patterns and Scaling in Nature and Society, 9:3 (2001), 329  crossref  isi  elib  scopus  scopus
    5. Li, WV, “Capture time of Brownian pursuits”, Probability Theory and Related Fields, 121:1 (2001), 30  crossref  mathscinet  isi  elib  scopus  scopus
    6. V. R. Fatalov, “Constants in the asymptotics of small deviation probabilities for Gaussian processes and fields”, Russian Math. Surveys, 58:4 (2003), 725–772  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. György Steinbrecher, B. Weyssow, “Generalized Randomly Amplified Linear System Driven by Gaussian Noises: Extreme Heavy Tail and Algebraic Correlation Decay in Plasma Turbulence”, Phys Rev Letters, 92:12 (2004), 125003  crossref  isi  scopus
    8. Mishura, YS, “Wiener integration with respect to fractional brownian motion”, Stochastic Calculus For Fractional Brownian Motion and Related Processes, 1929 (2008), 1  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. S C Lim, L P Teo, “Modeling single-file diffusion with step fractional Brownian motion and a generalized fractional Langevin equation”, J Stat Mech Theor Exp, 2009:8 (2009), P08015  crossref  isi  elib  scopus  scopus
    10. Ming Li, “Fractal Time Series-A Tutorial Review”, Math Probl Eng, 2010 (2010), 157264  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Steinbrecher G., Weyssow B., “New Representation and Generation Algorithm for Persistent Fractional Brownian Motion”, Romanian J Phys, 55:9–10 (2010), 1121–1131  mathscinet  zmath  isi  elib
    12. Aurzada F., “On the One-Sided Exit Problem for Fractional Brownian Motion”, Electron Commun Probab, 16 (2011), 392–404  crossref  mathscinet  zmath  isi  elib  scopus
    13. V. R. Fatalov, “Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the $L^p$ norm, $2\le p\le\infty$”, Theoret. and Math. Phys., 173:3 (2012), 1720–1733  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    14. Li M., “On the Long-Range Dependence of Fractional Brownian Motion”, Math. Probl. Eng., 2013, 842197  crossref  mathscinet  zmath  isi  scopus
    15. Delorme M., Wiese K.J., “Maximum of a Fractional Brownian Motion: Analytic Results From Perturbation Theory”, 115, no. 21, 2015, 210601  crossref  mathscinet  isi  scopus
    16. Delorme M., Wiese K.J., “Perturbative expansion for the maximum of fractional Brownian motion”, Phys. Rev. E, 94:1 (2016), 012134  crossref  isi  elib  scopus
    17. Delorme M., Wiese K.J., “Extreme-value statistics of fractional Brownian motion bridges”, Phys. Rev. E, 94:5 (2016), 052105  crossref  isi  elib  scopus
    18. Makogin V., “Simulation Paradoxes Related to a Fractional Brownian Motion With Small Hurst Index”, Mod. Stoch. Theory Appl., 3:2 (2016), 181–190  crossref  mathscinet  zmath  isi
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