EJP Reading Tools

Limit theorems for infinite-dimensional piecewise deterministic Markov processes. Applications to stochastic excitable membrane models

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Limit theorems for infinite-dimensional piecewise deterministic Markov processes. Applications to stochastic excitable membrane models
2.	Creator	Author's name, affiliation, country	Martin Georg Riedler; Johannes Kepler Universität; Austria
2.	Creator	Author's name, affiliation, country	Michèle Thieullen; Université Pierre et Marie Curie; France
2.	Creator	Author's name, affiliation, country	Gilles Wainrib; Université Paris 13; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Piecewise Deterministic Markov Processes; infinite-dimensional stochastic processes; law of large numbers; central limit theorem; excitable membrane models; random excitable media
3.	Subject	Subject classification	60J25; 60B12; 60F05; 92C20
4.	Description	Abstract	We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete random events are globally coupled with continuous space dependent variables solving partial differential equations, e.g., stochastic hybrid models of excitable membranes. We derive a law of large numbers which establishes a connection to deterministic macroscopic models and a martingale central limit theorem which connects the stochastic fluctuations to diffusion processes. As a prerequisite we carry out a thorough discussion of Hilbert space valued martingales associated to the PDMPs. Furthermore, these limit theorems provide the basis for a general Langevin approximation to PDMPs, i.e., stochastic partial differential equations that are expected to be similar in their dynamics to PDMPs. We apply these results to compartmental-type models of spatially extended excitable membranes. Ultimately this yields a system of stochastic partial differential equations which models the internal noise of a biological excitable membrane based on a theoretical derivation from exact stochastic hybrid models.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Agence Nationale de la Recherche, Engineering and Physical Sciences Research Council
7.	Date	(YYYY-MM-DD)	2012-07-18
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/1946
10.	Identifier	Digital Object Identifier	10.1214/EJP.v17-1946
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 17
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
15.	Rights	Copyright and permissions	The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free to copy, distribute, display, and perform the work to make derivative works to make commercial use of the work under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.