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On stochastic integration by series of Wiener integrals

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Abstract

Stochastic integrals of random functions with respect to a white-noise random measure are defined in terms of random series of usual Wiener integrals. Conditions for the existence of such integrals are obtained in terms of the nuclearity of certain operators onL 2-spaces. The relation with the Fisk-Stratonovich symmetric integral is also discussed.

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Author notes

  1. Jan Rosinski

    Present address: University of Tennessee, 37996-1300, Knoxville, TN, USA

Authors and Affiliations

  1. Center for Stochastic Processes, Department of Statistics, University of North Carolina, 27514, Chapel Hill, NC, USA

    Jan Rosinski

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  1. Jan Rosinski
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Additional information

This research was supported by AFOSR Contract No. F49620 82 C 0009.

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Rosinski, J. On stochastic integration by series of Wiener integrals. Appl Math Optim 19, 137–155 (1989). https://doi.org/10.1007/BF01448196

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  • DOI: https://doi.org/10.1007/BF01448196

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