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An Isometric Approach to Generalized Stochastic Integrals

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Abstract

The possibility to extend the classical Ito's construction of stochastic integrals is studied. This construction can be applied to fractional Brownian motions with Hurst index H∈(0, 1/2). A change of variables formula for fractional Brownian motions in terms of the stochastic integrals is given.

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Authors and Affiliations

  1. Department of Mathematics, Kiev University, 01033, Kiev, Ukraine

    Yulia Mishura

  2. Department of Mathematics, University of Helsinki, P.O. Box 4, FIN-00014, Finland

    Esko Valkeila

Authors
  1. Yulia Mishura
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  2. Esko Valkeila
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Mishura, Y., Valkeila, E. An Isometric Approach to Generalized Stochastic Integrals. Journal of Theoretical Probability 13, 673–693 (2000). https://doi.org/10.1023/A:1007854310936

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  • DOI: https://doi.org/10.1023/A:1007854310936

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