Occupation time functionals for a diffusion process or a
birth-and-death process on the edges of a graph $\Gamma$ depending only on the
values of the process on a part $\Gamma' \subset \Gamma$ of $\Gamma$ are
closely related to so-called eigenvalue depending boundary conditions for the
resolvent of the process. Under the assumption that the connected components of
$\Gamma\backslash\Gamma'$ are trees, we use the special structure of these
boundary conditions to give a procedure that replaces each of the trees by only
one edge and that associates this edge with a speed measure such that the
respective functional for the appearing process on the simplified graph
coincides with the original one.
Publié le : 2001-05-14
Classification:
Occupation time functionals,
diffusion process on a graph,
boundary value problems,
Titchmarsh-Weyl coefficient,
60J55,
60J60,
60J27
@article{1015345303,
author = {Weber, Matthias},
title = {On occupation time functionals for diffusion processes and
birth-and-death processes on graphs},
journal = {Ann. Appl. Probab.},
volume = {11},
number = {2},
year = {2001},
pages = { 544-567},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345303}
}
Weber, Matthias. On occupation time functionals for diffusion processes and
birth-and-death processes on graphs. Ann. Appl. Probab., Tome 11 (2001) no. 2, pp. 544-567. http://gdmltest.u-ga.fr/item/1015345303/