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On a Multiple Stratonovich-type Integral for Some Gaussian Processes

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Abstract

We construct a multiple Stratonovich-type integral with respect to Gaussian processes with covariance function of bounded variation. This construction is based on the previous definition of the multiple Itô-type integral given by Huang and Cambanis [Ann. Propab. 6(4), 585–614] and on a Hu–Meyer formula (that is, an expression of the multiple Stratonovich integral as a sum of Itô-type integrals of inferior or equal order) for the elementary functions. We also apply our results to the fractional Brownian motion with Hurst parameter \(H > \frac{1}{2}\).

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  1. Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain

    Maria Jolis

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  1. Maria Jolis
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Jolis, M. On a Multiple Stratonovich-type Integral for Some Gaussian Processes. J Theor Probab 19, 121–133 (2006). https://doi.org/10.1007/s10959-006-0006-5

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  • DOI: https://doi.org/10.1007/s10959-006-0006-5

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