Reflecting Brownian snake and a Neumann-Dirichlet problem

Romain Abraham

Stochastic Processes and their Applications, 2000, vol. 89, issue 2, 239-260

Abstract: The paper deals with a path-valued Markov process: the reflecting Brownian snake. It is a particular case of the path-valued process previously introduced by Le Gall. Here the spatial motion is a reflecting Brownian motion in a domain D of . Using this probabilistic tool, we construct an explicit function v solution of an integral equation which is, under some hypotheses on the regularity of v, equivalent to a semi-linear partial differential equation in D with some mixed Neumann-Dirichlet conditions on the boundary. When the hypotheses on v are not satisfied, we prove that v is still solution of a weak formulation of the Neumann-Dirichlet problem.

Keywords: Brownian; snake; Reflecting; Brownian; motion; Semi-linear; partial; differential; equations; Neumann; problem (search for similar items in EconPapers)
Date: 2000
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(00)00027-2
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:89:y:2000:i:2:p:239-260

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().