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Article: Linear diffusion with stationary switching regime

TitleLinear diffusion with stationary switching regime
Authors
KeywordsErgodicity
Existence of moments
Jump process
Markov switching
Ornstein-Uhlenbeck diffusion
Random difference equations
Issue Date2004
PublisherE D P Sciences. The Journal's web site is located at http://www.edpsciences.org
Citation
Esaim - Probability And Statistics, 2004, v. 8, p. 25-35 How to Cite?
AbstractLet Y be a Ornstein-Uhlenbeck diffusion governed by a stationary and ergodic process X : dYt = a(Xt)Ytdt + =(X t)dWt,Y0 = y0. We establish that under the condition α = Eμ(a(X0)) < 0 with n the stationary distribution of the regime process X, the diffusion Y is ergodic. We also consider conditions for the existence of moments for the invariant law of Y when X is a Markov jump process having a finite number of states. Using results on random difference equations on one hand and the fact that conditionally to X, Y is Gaussian on the other hand, we give such a condition for the existence of the moment of order s ≥ 0. Actually we recover in this case a result that Basak et al. [J. Math. Anal. Appl. 202 (1996) 604-622] have established using the theory of stochastic control of linear systems.
Persistent Identifierhttp://hdl.handle.net/10722/132624
ISSN
2015 Impact Factor: 0.6
2015 SCImago Journal Rankings: 1.031

 

DC FieldValueLanguage
dc.contributor.authorGuyon, Xen_HK
dc.contributor.authorIovleff, Sen_HK
dc.contributor.authorYao, JFen_HK
dc.date.accessioned2011-03-28T09:27:05Z-
dc.date.available2011-03-28T09:27:05Z-
dc.date.issued2004en_HK
dc.identifier.citationEsaim - Probability And Statistics, 2004, v. 8, p. 25-35en_HK
dc.identifier.issn1292-8100en_HK
dc.identifier.urihttp://hdl.handle.net/10722/132624-
dc.description.abstractLet Y be a Ornstein-Uhlenbeck diffusion governed by a stationary and ergodic process X : dYt = a(Xt)Ytdt + =(X t)dWt,Y0 = y0. We establish that under the condition α = Eμ(a(X0)) < 0 with n the stationary distribution of the regime process X, the diffusion Y is ergodic. We also consider conditions for the existence of moments for the invariant law of Y when X is a Markov jump process having a finite number of states. Using results on random difference equations on one hand and the fact that conditionally to X, Y is Gaussian on the other hand, we give such a condition for the existence of the moment of order s ≥ 0. Actually we recover in this case a result that Basak et al. [J. Math. Anal. Appl. 202 (1996) 604-622] have established using the theory of stochastic control of linear systems.en_HK
dc.languageengen_US
dc.publisherE D P Sciences. The Journal's web site is located at http://www.edpsciences.orgen_HK
dc.relation.ispartofESAIM - Probability and Statisticsen_HK
dc.subjectErgodicityen_HK
dc.subjectExistence of momentsen_HK
dc.subjectJump processen_HK
dc.subjectMarkov switchingen_HK
dc.subjectOrnstein-Uhlenbeck diffusionen_HK
dc.subjectRandom difference equationsen_HK
dc.titleLinear diffusion with stationary switching regimeen_HK
dc.typeArticleen_HK
dc.identifier.emailYao, JF: jeffyao@hku.hken_HK
dc.identifier.authorityYao, JF=rp01473en_HK
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1051/ps:2003017en_HK
dc.identifier.scopuseid_2-s2.0-13444250981en_HK
dc.identifier.volume8en_HK
dc.identifier.spage25en_HK
dc.identifier.epage35en_HK
dc.publisher.placeFranceen_HK
dc.identifier.scopusauthoridGuyon, X=6602587667en_HK
dc.identifier.scopusauthoridIovleff, S=6507904723en_HK
dc.identifier.scopusauthoridYao, JF=7403503451en_HK

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