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The two-parameter Volterra multifractional process

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  • Mendy, Ibrahima
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    Abstract

    In the case where the parameters H1 and H2 belong to (1/2,1), Feyel and De La Pradelle (1991) have introduced a representation of the usual fractional Brownian sheet {Bs,tH1,H2}(s,t)∈R+2, as a stochastic integral over the compact rectangle [0,s]×[0,t], with respect to the Brownian sheet. In this paper, we introduce the so-called two-parameter Volterra multifractional process by replacing in the latter representation of {Bs,tH1,H2}(s,t)∈R+2 the constant parameters H1 and H2 by two Hölder functions α(s) and β(t) with values in (1/2,1). We obtain that the pointwise and the local Hölder exponents of the two-parameter Volterra multifractional process at any point (s0,t0) are equal to min(α(s0),β(t0)).

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 12 ()
    Pages: 2115-2124

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2115-2124

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    Keywords: Fractional Brownian sheet; Volterra; Multifractional process;

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    1. Antoine Ayache & Jacques Vehel, 2000. "The Generalized Multifractional Brownian Motion," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 7-18, January.
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