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On matching diffusions, Laplace transforms and partial differential equations

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  • Jakubowski, Jacek
  • Wiśniewolski, Maciej

Abstract

We present the idea of intertwining of two diffusions by Feynman–Kac operators. We present implications of the method and give its applications. The examples give new results on stochastic processes including a generalized squared Bessel processes. We present a version of the method and its applications to PDE of the second order. A new dependence between diffusions and solutions of hyperbolic PDE is presented. The version of Feynman–Kac representation for hyperbolic PDE is given. It is presented the simple form of Laplace transform of wave equation with axial symmetry.

Suggested Citation

  • Jakubowski, Jacek & Wiśniewolski, Maciej, 2015. "On matching diffusions, Laplace transforms and partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3663-3690.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:10:p:3663-3690
    DOI: 10.1016/j.spa.2015.04.003
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    References listed on IDEAS

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    1. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
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