On matching diffusions, Laplace transforms and partial differential equations

Jacek Jakubowski and Maciej Wiśniewolski

Stochastic Processes and their Applications, 2015, vol. 125, issue 10, 3663-3690

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.

Keywords: Brownian motion; Squared Bessel process; Laplace transform; Diffusion; Feynman–Kac theorem; Partial differential equations (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spa.2015.04.003

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