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 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

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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
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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. 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
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
3. Jost C., “A note on ergodic transformations of self–similar Volterra Gaussian processes”, Electronic Communications in Probability, 12 (2007), 259–266
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
5. Mishura Yu., Valkeila E., “An Extension of the Levy Characterization to Fractional Brownian Motion”, Ann Probab, 39:2 (2011), 439–470
6. Picard J., “Representation Formulae for the Fractional Brownian Motion”, Seminaire de Probabilites XLIII, Lecture Notes in Mathematics, 2006, 2011, 3–70
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
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
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