Translator Disclaimer
May 2001 On occupation time functionals for diffusion processes and birth-and-death processes on graphs
Matthias Weber
Ann. Appl. Probab. 11(2): 544-567 (May 2001). DOI: 10.1214/aoap/1015345303

Abstract

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.

Citation

Download Citation

Matthias Weber. "On occupation time functionals for diffusion processes and birth-and-death processes on graphs." Ann. Appl. Probab. 11 (2) 544 - 567, May 2001. https://doi.org/10.1214/aoap/1015345303

Information

Published: May 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1020.60068
MathSciNet: MR1843057
Digital Object Identifier: 10.1214/aoap/1015345303

Subjects:
Primary: 60J27, 60J55, 60J60

Rights: Copyright © 2001 Institute of Mathematical Statistics

JOURNAL ARTICLE
24 PAGES


SHARE
Vol.11 • No. 2 • May 2001
Back to Top