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On Stochastic Variation in Discrete Time Systems

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Computer Aided Systems Theory - EUROCAST 2009 (EUROCAST 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5717))

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Abstract

This paper concerns with the variation in discrete time systems driven by a random walk, in contrast with the ordinary Malliavin calculus based on a Brownian motion. A derivative of random functionals with respect to a random walk is introduced and some its fundamental properties are shown. Theories parallel to Malliavin calculus are also discussed in view of applications for discrete time phenomena in signal processing, mathematical finance, and systems science and engineering.

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References

  1. Carmona, R.A., Tehranchi, M.R.: Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective. Springer, Berlin (2006)

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  3. Malliavin, P., Thalmaier, A.: Stochastic Calculus of Variations in Mathematical Finance. Springer, Berlin (2006)

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  5. Di Nunno, G., Øksendal, B., Proske, F.: Malliavin Calculus for Lévy Processes with Applications to Finance. Springer, Heidelberg (2009)

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Author information

Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Chuo University, Tokyo, 112-8551, Japan

    Yasushi Endow

Authors
  1. Yasushi Endow
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Editor information

Editors and Affiliations

  1. Instituto Universitario de Ciencias y Tecnologías Cibernéticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira, 35017, Las Palmas de Gran Canaria, Las Palmas, Spain

    Roberto Moreno-Díaz  & Alexis Quesada-Arencibia  & 

  2. Institute of Systems Science, Johannes Kepler University Linz, Altenbergerstrasse 69, 4040, Linz, Austria

    Franz Pichler

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© 2009 Springer-Verlag Berlin Heidelberg

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Endow, Y. (2009). On Stochastic Variation in Discrete Time Systems. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory - EUROCAST 2009. EUROCAST 2009. Lecture Notes in Computer Science, vol 5717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04772-5_64

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  • DOI: https://doi.org/10.1007/978-3-642-04772-5_64

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04771-8

  • Online ISBN: 978-3-642-04772-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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