On occupation time functionals for diffusion processes and birth-and-deathprocesses on graphs

Authors
Citation
M. Weber, On occupation time functionals for diffusion processes and birth-and-deathprocesses on graphs, ANN APPL PR, 11(2), 2001, pp. 544-567
Citations number
29
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
ANNALS OF APPLIED PROBABILITY
ISSN journal
1050-5164 → ACNP
Volume
11
Issue
2
Year of publication
2001
Pages
544 - 567
Database
ISI
SICI code
1050-5164(200105)11:2<544:OOTFFD>2.0.ZU;2-9
Abstract
Occupation time functionals for a diffusion process or a birth-and-death pr ocess on the edges of a graph Gamma depending only on the values of the pro cess on a part Gamma ' subset of Gamma of Gamma are closely related to so-c alled eigenvalue depending boundary conditions for the resolvent of the pro cess. Under the assumption that the connected components of Gamma \ Gamma ' are trees, we use the special structure of these boundary conditions to gi ve a procedure that replaces each of the trees by only one edge and that as sociates this edge with a speed measure such that the respective functional for the appearing process on the simplified graph coincides with the origi nal one.