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Nonhomogeneous First-order Linear Malliavin Type Differential Equation

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Pseudo-Differential Operators, Generalized Functions and Asymptotics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 231))

Abstract

In this paper we solve a nonhomogeneous first-order linear equation involving the Malliavin derivative operator with stochastic coefficients by use of the chaos expansion method. We prove existence and uniqueness of a solution in a certain weighted space of generalized stochastic distributions and represent the obtained solution in the Wiener-ItÔ chaos expansion form.

Mathematics Subject Classification (2010). Primary: 60H15, 60H40, 60H10, 60H07, 60G20.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Informatics Faculty of Traffic and Transport Engineering, University of Belgrade, Belgrade, Serbia

    Tijana Levajković

  2. Department of Mathematics and Informatics Faculty of Science, University of Novi Sad, Belgrade, Serbia

    Dora Seleši

Authors
  1. Tijana Levajković
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  2. Dora Seleši
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Corresponding author

Correspondence to Tijana Levajković .

Editor information

Editors and Affiliations

  1. , Department of Mathematics and Statistics, Queen's University, University Avenue, Jeffery Hall, Kingston, K7L 3N6, Ontario, Canada

    Shahla Molahajloo

  2. , Dept. of Mathematics & Informatics, University of Novi Sad, Trg Dsiteja Obradovica 4, Novi Sad, 21000, Serbia

    Stevan Pilipović

  3. Dept. of Computer Science, Physics, and Mathematics, Linnæus University, Vejdes Plats 6, Växjö, 351 95, Sweden

    Joachim Toft

  4. Department of Mathematics & Statistics, York University, Keele Street 4700, Toronto, M3J 1P3, Ontario, Canada

    M. W. Wong

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Levajković, T., Seleši, D. (2013). Nonhomogeneous First-order Linear Malliavin Type Differential Equation. In: Molahajloo, S., Pilipović, S., Toft, J., Wong, M. (eds) Pseudo-Differential Operators, Generalized Functions and Asymptotics. Operator Theory: Advances and Applications, vol 231. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0585-8_20

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