2014/10/17 by Maciej Wiśniewolski, Wiśniewolski, Maciej, Jacek Jakubowski +1
Economics, Econometrics and Finance · Mathematics · #60H30 #60H35 #60J60 #60J70 #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1410.4858
openalex publication_date 2014/10/17 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We present the idea of intertwining of two diffusions by Feynman-Kac\noperators. We present some variations and implications of the method and give\nexamples of its applications. Among others, it turns out to be a very useful\ntool for finding the expectations of some functionals of diffusions, especially\nfor computing the Laplace transforms of stochastic processes. The examples give\nnew results on marginal distributions of many stochastic processes including a\ngeneralized squared Bessel processes and joint distribution for squared Bessel\nbridge and its integral - the close formulae of the Laplace transforms are\npresented. We finally present a general version of the method and its\napplications to PDE of the second order. A new dependence between diffusions\nand solutions of hyperbolic partial differential equations is presented. In\nparticular, the version of Feynman-Kac representation for hyperbolic PDE is\ngiven. It is presented, among others, the simple form of Laplace transform of\nwave equation with axial symmetry.\n