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., 2002, Volume 47, Issue 1, Pages 59–70 (Mi tvp2985)  

This article is cited in 8 scientific papers (total in 8 papers)

Linear problems for a fractional Brownian motion: Group approach

G. M. Molchan

Observatoire de la Côte d'Azur

Abstract: For the fractional Brownian motion (fBm) the problem of extrapolation from a segment, the canonical representation of fBm via white noise on a segment and their reciprocal relation, and Girsanov's formula are considered. A general approach to these problems is based on the invariance of fBm with respect to linear rational transformations of time. This approach practically excludes the solution of integral equations and explains the efficiency of the aforementioned problems for fBm.

Keywords: fractional Brownian motion, extrapolation, Girsanov's formula.

DOI: https://doi.org/10.4213/tvp2985

Full text: PDF file (1183 kB)

English version:
Theory of Probability and its Applications, 2003, 47:1, 69–78

Bibliographic databases:

Received: 08.09.2000

Citation: G. M. Molchan, “Linear problems for a fractional Brownian motion: Group approach”, Teor. Veroyatnost. i Primenen., 47:1 (2002), 59–70; Theory Probab. Appl., 47:1 (2003), 69–78

Citation in format AMSBIB
\Bibitem{Mol02}
\by G.~M.~Molchan
\paper Linear problems for a fractional Brownian motion: Group approach
\jour Teor. Veroyatnost. i Primenen.
\yr 2002
\vol 47
\issue 1
\pages 59--70
\mathnet{http://mi.mathnet.ru/tvp2985}
\crossref{https://doi.org/10.4213/tvp2985}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1978695}
\zmath{https://zbmath.org/?q=an:1035.60084}
\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 1
\pages 69--78
\crossref{https://doi.org/S0040585X97979445}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000183800400005}


Linking options:
  • http://mi.mathnet.ru/eng/tvp2985
  • https://doi.org/10.4213/tvp2985
  • http://mi.mathnet.ru/eng/tvp/v47/i1/p59

    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. Dzhaparidze K., van Zanten H., Zareba P., “Representations of fractional Brownian motion using vibrating strings”, Stochastic Processes and Their Applications, 115:12 (2005), 1928–1953  crossref  mathscinet  zmath  isi  scopus
    2. Dzhaparidze K., van Zanten H., “Krein's spectral theory and the Paley–Wiener expansion for fractional Brownian motion”, Annals of Probability, 33:2 (2005), 620–644  crossref  mathscinet  zmath  isi  scopus
    3. Jost C., “A note on ergodic transformations of self–similar Volterra Gaussian processes”, Electronic Communications in Probability, 12 (2007), 259–266  crossref  mathscinet  zmath  isi  scopus
    4. Mishura Yu.S., “Wiener integration with respect to fractional brownian motion”, Stochastic Calculus for Fractional Brownian Motion and Related Processes, Lecture Notes in Mathematics, 1929, 2008, 1  crossref  mathscinet  adsnasa  isi  scopus
    5. Mishura Yu., Valkeila E., “An Extension of the Levy Characterization to Fractional Brownian Motion”, Ann Probab, 39:2 (2011), 439–470  crossref  mathscinet  zmath  isi  scopus
    6. Picard J., “Representation Formulae for the Fractional Brownian Motion”, Seminaire de Probabilites XLIII, Lecture Notes in Mathematics, 2006, 2011, 3–70  crossref  mathscinet  zmath  isi  scopus
    7. Pipiras V. Taqqu M., “Long-Range Dependence and Self-Similarity”, Long-Range Dependence and Self-Similarity, Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge Univ Press, 2017, 1–668  crossref  mathscinet  zmath  isi
    8. Mishura Yu., Shklyar S., “Distance Between the Fractional Brownian Motion and the Space of Adapted Gaussian Martingales”, Nonlinear Anal.-Model Control, 24:4 (2019), 639–657  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:242
    Full text:62

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