Geodesic
Killed Random Processes and Heat Kernels
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 423-432 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $V(x)\geq0$ be a given function tending to a constant at infinity. It is well known that the density of the Brownian motion $B_t$ killed at the infinitesimal rate $V$ is a Green's function for the heat operator with such a potential. With an appropriate generalization, its Laplace transform also gives the density of $\int_0^tV(B_s)ds$. We construct such a Green's function via spectral analysis of the classical one-dimensional stationary Schrodinger operator.
Keywords: Brownian motion, heat equation propagator. 
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Kh. Villarroel. Killed Random Processes and Heat Kernels. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 423-432. http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a19/

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