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Characterization of the Ito Integral

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  • Lars Tyge Nielsen

Abstract

This paper provides an existence-and-uniqueness theorem characterizing the stochastic integral with respect to a Wiener process. The integral is represented as a mapping from the space of measurable and adapted pathwise locally integrable processes to the space of continuous adapted processes. It is characterized in terms of two properties: (1) how the stochastic integrals of simple processes are calculated and (2) how these integrals converge in probability when the time integrals of the squared integrands converge in probability.

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  • Lars Tyge Nielsen, 2018. "Characterization of the Ito Integral," Papers 1812.09637, arXiv.org.
    • Handle: RePEc:arx:papers:1812.09637
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    1. Nielsen, Lars Tyge, 1999. "Pricing and Hedging of Derivative Securities," OUP Catalogue, Oxford University Press, number 9780198776192.
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