Boundary value problems and Markov processes
This volume is devoted to a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel' boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an inte...
Kaydedildi:
| Yazar: | |
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| Materyal Türü: | Livre numérique |
| Dil: | Anglais |
| Baskı/Yayın Bilgisi: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edisyon: | 2nd ed. 2009. |
| Seri Bilgileri: | Lecture Notes in Mathematics
1499 |
| Konular: | |
| Online Erişim: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Not: |
Ouvrage dédié à la mémoire du Pr Kiyosi Itô (1915-2008) Description d'après consultation du 04 octobre 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Boundary Value Problems and Markov Processes, Texte imprimé, 9783642023712 • Boundary value problems and Markov processes, Kazuaki Taira, 2nd edition, 2009, Berlin, Springer, 1 vol. (XII-186 p.), Lecture notes in mathematics, 978-3-642-01676-9 |
| Özet: | This volume is devoted to a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel' boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-differential operator, called a Waldenfels operator, in the interior of the domain, and it obeys a boundary condition, called the Ventcel' boundary condition, on the boundary of the domain. Probabilistically, a Markovian particle moves both by jumps and continuously in the state space and it obeys the Ventcel' boundary condition, which consists of six terms corresponding to the diffusion along the boundary, the absorption phenomenon, the reflection phenomenon, the sticking (or viscosity) phenomenon, the jump phenomenon on the boundary, and the inward jump phenomenon from the boundary. In particular, second-order elliptic differential operators are called diffusion operators and describe analytically strong Markov processes with continuous paths in the state space such as Brownian motion. We observe that second-order elliptic differential operators with smooth coefficients arise naturally in connection with the problem of construction of Markov processes in probability. Since second-order elliptic differential operators are pseudo-differential operators, we can make use of the theory of pseudo-differential operators as in the previous book: Semigroups, boundary value problems and Markov processes (Springer-Verlag, 2004). Our approach here is distinguished by its extensive use of the ideas and techniques characteristic of the recent developments in the theory of partial differential equations. Several recent developments in the theory of singular integrals have made further progress in the study of elliptic boundary value problems and hence in the study of Markov processes possible. The presentation of these new results is the main purpose of this book |
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| Diğer Bilgileri: | Ouvrage dédié à la mémoire du Pr Kiyosi Itô (1915-2008) Description d'après consultation du 04 octobre 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9783642016776 |
| ISSN: | 1617-9692 |
| Erişim: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |