On a Ogawa-type integral with application to the fractional bhownian motion

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Abstract

We construct a deterministic Ogawa-type integral with respect to a continuous function that, in particular, can be a trajectory of the Fractional Brownian motion. This integral is related with the Stratonovich integral and with the integrals introduced by Ciesielski et altri and Zȧhle. We give a sufficient condition for the integrability of a function in this sense, that does not imply its continuity. Under this sufficient condition, we obtain a Besov regularity property of the indefinite integral. We also study the stochastic Ogawa integral for stochastic processes when integrate with respect to the Fractional Brownian motion of Hurst parameter H ∈ (1/2, 1).
Original languageEnglish
Pages (from-to)617-634
JournalStochastic Analysis and Applications
Volume18
DOIs
Publication statusPublished - 1 Jan 2000

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