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Constructive Martingale Representation in Functional Itô Calculus: A Local Martingale Extension

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 271))

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Abstract

The constructive martingale representation theorem of functional Itô calculus is extended, from the space of square integrable martingales, to the space of local martingales. The setting is that of an augmented filtration generated by a Wiener process.

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Acknowledgements

The author is grateful to Mathias Lindholm for helpful discussions.

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Authors and Affiliations

  1. Department of Mathematics, Stockholm University, SE-106 91, Stockholm, Sweden

    Kristoffer Lindensjö

Authors
  1. Kristoffer Lindensjö
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Correspondence to Kristoffer Lindensjö .

Editor information

Editors and Affiliations

  1. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Sergei Silvestrov

  2. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Anatoliy Malyarenko

  3. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Milica Rančić

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Lindensjö, K. (2018). Constructive Martingale Representation in Functional Itô Calculus: A Local Martingale Extension. In: Silvestrov, S., Malyarenko, A., Rančić, M. (eds) Stochastic Processes and Applications. SPAS 2017. Springer Proceedings in Mathematics & Statistics, vol 271. Springer, Cham. https://doi.org/10.1007/978-3-030-02825-1_9

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