Geodesic
Killed Random Processes and Heat Kernels
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 423-432

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_2005_144_2_a19,
     author = {Kh. Villarroel},
     title = {Killed {Random} {Processes} and {Heat} {Kernels}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {423--432},
     publisher = {mathdoc},
     volume = {144},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a19/}
}
TY  - JOUR
AU  - Kh. Villarroel
TI  - Killed Random Processes and Heat Kernels
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2005
SP  - 423
EP  - 432
VL  - 144
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a19/
LA  - ru
ID  - TMF_2005_144_2_a19
ER  - 
%0 Journal Article
%A Kh. Villarroel
%T Killed Random Processes and Heat Kernels
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2005
%P 423-432
%V 144
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a19/
%G ru
%F TMF_2005_144_2_a19
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/