Semigroups, Boundary Value Problems and Markov Processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The purpose of this book is to provide a careful and accessible account along modern lines of the subject which the title deals, as well as to discuss problems of current interest in the field. Unlike many other books on Markov processes, this book focuses on the relationship between Markov processes and elliptic boundary value problems, with emphasis on the study of analytic semigroups. More precisely, this book is devoted to the functional analytic approach to a class of degenerate boundary value problems for second-order elliptic integro-differential operators, called Waldenfels operators, which includes as particular cases the Dirichlet and Robin problems. We prove that this class of boundary value problems provides a new example of analytic semigroups both in the LP topology and in the topology of uniform convergence. As an application, we construct a strong Markov process corresponding to such a physical phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it "dies" at the time when it reaches the set where the particle is definitely absorbed. The approach here is distinguished by the extensive use of the techniques characteristic of recent developments in the theory of partial differential equations. The main technique used is the calculus of pseudo-differential operators which may be considered as a modern theory of potentials |
| Beschreibung: | 1 Online-Ressource (XII, 340 p) |
| ISBN: | 9783662098578 9783642073717 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-3-662-09857-8 |
Internformat
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Datensatz im Suchindex
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| id | DE-604.BV042423426 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662098578 9783642073717 |
| issn | 1439-7382 |
| language | English |
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| physical | 1 Online-Ressource (XII, 340 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2004 |
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| publisher | Springer Berlin Heidelberg |
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| spelling | Taira, Kazuaki Verfasser aut Semigroups, Boundary Value Problems and Markov Processes by Kazuaki Taira Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (XII, 340 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 The purpose of this book is to provide a careful and accessible account along modern lines of the subject which the title deals, as well as to discuss problems of current interest in the field. Unlike many other books on Markov processes, this book focuses on the relationship between Markov processes and elliptic boundary value problems, with emphasis on the study of analytic semigroups. More precisely, this book is devoted to the functional analytic approach to a class of degenerate boundary value problems for second-order elliptic integro-differential operators, called Waldenfels operators, which includes as particular cases the Dirichlet and Robin problems. We prove that this class of boundary value problems provides a new example of analytic semigroups both in the LP topology and in the topology of uniform convergence. As an application, we construct a strong Markov process corresponding to such a physical phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it "dies" at the time when it reaches the set where the particle is definitely absorbed. The approach here is distinguished by the extensive use of the techniques characteristic of recent developments in the theory of partial differential equations. The main technique used is the calculus of pseudo-differential operators which may be considered as a modern theory of potentials Mathematics Harmonic analysis Functional analysis Differential equations, partial Distribution (Probability theory) Functional Analysis Abstract Harmonic Analysis Partial Differential Equations Probability Theory and Stochastic Processes Mathematik Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Analytische Halbgruppe (DE-588)4376792-8 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 s Analytische Halbgruppe (DE-588)4376792-8 s Markov-Prozess (DE-588)4134948-9 s 1\p DE-604 https://doi.org/10.1007/978-3-662-09857-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Taira, Kazuaki Semigroups, Boundary Value Problems and Markov Processes Mathematics Harmonic analysis Functional analysis Differential equations, partial Distribution (Probability theory) Functional Analysis Abstract Harmonic Analysis Partial Differential Equations Probability Theory and Stochastic Processes Mathematik Elliptisches Randwertproblem (DE-588)4193399-0 gnd Analytische Halbgruppe (DE-588)4376792-8 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| subject_GND | (DE-588)4193399-0 (DE-588)4376792-8 (DE-588)4134948-9 |
| title | Semigroups, Boundary Value Problems and Markov Processes |
| title_auth | Semigroups, Boundary Value Problems and Markov Processes |
| title_exact_search | Semigroups, Boundary Value Problems and Markov Processes |
| title_full | Semigroups, Boundary Value Problems and Markov Processes by Kazuaki Taira |
| title_fullStr | Semigroups, Boundary Value Problems and Markov Processes by Kazuaki Taira |
| title_full_unstemmed | Semigroups, Boundary Value Problems and Markov Processes by Kazuaki Taira |
| title_short | Semigroups, Boundary Value Problems and Markov Processes |
| title_sort | semigroups boundary value problems and markov processes |
| topic | Mathematics Harmonic analysis Functional analysis Differential equations, partial Distribution (Probability theory) Functional Analysis Abstract Harmonic Analysis Partial Differential Equations Probability Theory and Stochastic Processes Mathematik Elliptisches Randwertproblem (DE-588)4193399-0 gnd Analytische Halbgruppe (DE-588)4376792-8 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| topic_facet | Mathematics Harmonic analysis Functional analysis Differential equations, partial Distribution (Probability theory) Functional Analysis Abstract Harmonic Analysis Partial Differential Equations Probability Theory and Stochastic Processes Mathematik Elliptisches Randwertproblem Analytische Halbgruppe Markov-Prozess |
| url | https://doi.org/10.1007/978-3-662-09857-8 |
| work_keys_str_mv | AT tairakazuaki semigroupsboundaryvalueproblemsandmarkovprocesses |