Piecewise-deterministic Markov process: Difference between revisions

Revision as of 09:24, 15 November 2013

Revision as of 09:26, 15 November 2013

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==Applications==

PDMPs have been shown useful in [[ruin theory]],<ref>{{cite jstor|1427443}}</ref> [[queueing theory]],<ref>{{cite jstor|3214906}}</ref><ref>{{cite doi|10.1017/S0269964805050011}}</ref> for modelling [[biochemistry|biochemical processes]] such as subtilin production by the organism [[B. subtilis]] and DNA replication in [[eukaryotes]]<ref>{{cite book|chapter=Chapter 9. Stochastic Hybrid Modeling of Biochemical Processes|chapterurl=http://www.nt.ntnu.no/users/skoge/prost/proceedings/hygea-workshop-july07-systems_biology/publications/JL2/Chapter9.pdf|title=Stochastic Hybrid Systems|first1=Christos G.|last1=Cassandras|first2=John|last2=Lygeros|publisher=CRC Press|year=2007|isbn=9780849390838}}</ref> for modelling [[earthquake]]s<ref>{{cite doi|10.1016/0304-4149(84)90009-7}}</ref>. Moreover, this class of processes has been shown to be appropriate for biophysical neuron models with stochastic ion channels<ref>{{cite webjournal|urllast=https://19803173-a-62cb3a1a-s-sitesPakdaman|first=K.googlegroups|coauthors=Thieullen, M.com/site/gwainrib/papers/fluidlimit; Wainrib, G.pdf?attachauth|title=ANoY7co5_XhD_K19_Ybbw4UdrJaKLai6UgjkYCZv9FNp-Pki6M9U2SGMCip5UPv4n3OfRvNHIrTrht72sZ38FLqDwtGBkJFUx5vKOowXjsGpOoHcqGtMU3HbVDWdXDglPYfQUY-jl78EKSnAAfNdZRDrmEh0zPNX68Y4L8sO4F6nZiBXp0W9031HPn3uamoPD2wZz_ooKjZ54BH0j0rI6gffYIVmGYExBA%3D%3D&attredirectsFluid limit theorems for stochastic hybrid systems with application to neuron models|journal=0Advances in Applied Probability|year=2010|month=September|volume=42|issue=3|pages=761–794|doi=10.1239/aap/1282924062}}</ref>.

==Properties==