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Multilayer heat equations and their solutions via oscillating integral transforms

Author

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  • Itkin, Andrey
  • Lipton, Alexander
  • Muravey, Dmitry

Abstract

By expanding the Dirac delta function in terms of the eigenfunctions of the corresponding Sturm–Liouville problem, we construct some new (oscillating) integral transforms. These transforms are then used to solve various finance, physics, and mathematics problems, which could be characterized by the existence of a multilayer spatial structure and moving (time-dependent) boundaries (internal interfaces) between the layers. Thus, constructed solutions are semi-analytical and extend the authors’ previous work (Itkin, Lipton, Muravey, Multilayer heat equations: Application to finance, FMF, 1, 2021). However, our new method does not duplicate the previous one but provides alternative representations of the solution which have different properties and serve other purposes.

Suggested Citation

  • Itkin, Andrey & Lipton, Alexander & Muravey, Dmitry, 2022. "Multilayer heat equations and their solutions via oscillating integral transforms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).
    • Handle: RePEc:eee:phsmap:v:601:y:2022:i:c:s0378437122003806
    DOI: 10.1016/j.physa.2022.127544
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    References listed on IDEAS

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    1. Carr, Elliot J. & March, Nathan G., 2018. "Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 286-303.
    2. A. Itkin & A. Lipton & D. Muravey, 2021. "Multilayer heat equations: application to finance," Papers 2102.08338, arXiv.org.
    3. Andrey Itkin & Alexander Lipton & Dmitry Muravey, 2021. "Generalized Integral Transforms in Mathematical Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 12147, August.
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    Citations

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    Cited by:

    1. Antoine Lejay & Sara Mazzonetto, 2024. "Maximum likelihood estimator for skew Brownian motion: The convergence rate," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(2), pages 612-642, June.
    2. Andrey Itkin, 2023. "Semi-analytic pricing of American options in time-dependent jump-diffusion models with exponential jumps," Papers 2308.08760, arXiv.org, revised Feb 2024.

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