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Probability in Banach Spaces, 9 pp 73–89Cite as

Birkhäuser

Random Fractals Generated by Oscillations of Processes with Stationary and Independent Increments

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Part of the book series: Progress in Probability ((PRPR,volume 35))

Abstract

Let {W(t) : t ≥ 0} denote a standard Wiener process, and for any Λ ∈ [0,1], set

$$E(\Lambda )=\left \{ t \in[0,1): \limsup_{h\downarrow 0}(2h \log(1/h))^{-1/2}(W(t+h)-W(t))\geq\Lambda \right \}$$

.

Research supported by an NSF grant and the Alexamder von Humboldt Foundation.

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Author information

Authors and Affiliations

  1. L.S.T.A., Université Paris VI, 4 Place Jussieu, 75252, Paris, Cedex 05, France

    Paul Deheuvels

  2. Department of Mathematical Sciences, University of Delaware, 501 Ewing Hall, Newark, DE, 19716, USA

    David M. Mason

Authors
  1. Paul Deheuvels
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  2. David M. Mason
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Editor information

Editors and Affiliations

  1. Mathematical Institute, Aarhus University, NY Munkegade, DK-8000, Aarhus C, Denmark

    Jørgen Hoffmann-Jørgensen

  2. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    James Kuelbs

  3. Department of Mathematics, City College of New York, New York, NY, 10031, USA

    Michael B. Marcus

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© 1994 Springer Science+Business Media New York

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Deheuvels, P., Mason, D.M. (1994). Random Fractals Generated by Oscillations of Processes with Stationary and Independent Increments. In: Hoffmann-Jørgensen, J., Kuelbs, J., Marcus, M.B. (eds) Probability in Banach Spaces, 9. Progress in Probability, vol 35. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0253-0_5

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  • DOI: https://doi.org/10.1007/978-1-4612-0253-0_5

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6682-2

  • Online ISBN: 978-1-4612-0253-0

  • eBook Packages: Springer Book Archive

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