UID:
almahu_9947359997202882
Format:
Online-Ressource (X, 284 S.)
ISBN:
9783110302004 (print)
Series Statement:
De Gruyter Studies in Mathematics 48
Content:
Biographical note: Y. Oshima, Kumamoto University, Japan.
Content:
Biographical note: Y. Oshima, Kumamoto University.
Content:
Main description: Symmetric Dirichlet forms andtheir associated Markov processes are important and powerful toolsin the theory of Markovprocesses and their applications. In this monograph, wegeneralize the theory to non-symmetric and time dependent semi-Dirichlet forms. Thus, we can cover the wide class of Markov processes and analytic theory which do not possess the dualMarkov processes.
Content:
Symmetric Dirichlet forms andtheir associated Markov processes are important and powerful toolsin the theory of Markovprocesses and their applications. In this monograph, wegeneralize the theory to non-symmetric and time dependent semi-Dirichlet forms. Thus, we can cover the wide class of Markov processes and analytic theory which do not possess the dualMarkov processes
Note:
Description based upon print version of record
,
3.4 Negligible sets for Hunt processes3.5 Decompositions of Dirichlet forms; 4 Additive functionals and smooth measures; 4.1 Positive continuous additive functionals; 4.2 Dual PCAFs and duality relations; 4.3 Time changes and killings; 5 Martingale AFs and AFs of zero energy; 5.1 Fukushima's decomposition of AFs; 5.1.1 AFs generated by functions of ℱ; 5.1.2 Martingale additive functionals of finite energy; 5.1.3 CAFs of zero energy; 5.2 Beurling-Deny type decomposition; 5.3 CAFs of locally zero energy in the weak sense; 5.4 Martingale AFs of strongly local Dirichlet forms.
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5.5 Transformations by multiplicative functionals5.6 Conservativeness and recurrence of Dirichlet forms; 6 Time dependent Dirichlet forms; 6.1 Time dependent Dirichlet forms and associated resolvents; 6.2 A parabolic potential theory; 6.3 Associated space-time processes; 6.4 Additive functionals and associated measures; 6.5 Some stochastic calculus; Notes; Bibliography; Index.
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Preface; 1 Dirichlet forms; 1.1 Semi-Dirichlet forms and resolvents; 1.2 Closability and regular Dirichlet forms; 1.3 Transience and recurrence of Dirichlet forms; 1.4 An auxiliary bilinear form; 1.5 Examples; 1.5.1 Diffusion case; 1.5.2 Jump type case; 2 Some analytic properties of Dirichlet forms; 2.1 Capacity; 2.2 Quasi-Continuity; 2.3 Potential of measures; 2.4 An orthogonal decomposition of the Dirichlet forms; 3 Markov processes; 3.1 Hunt processes; 3.2 Excessive functions and negligible sets; 3.3 Hunt processes associated with a regular Dirichlet form.
Additional Edition:
ISBN 9783110302066
Additional Edition:
ISBN 9783110302073
Language:
English
Keywords:
Electronic books
DOI:
10.1515/9783110302066
URL:
http://dx.doi.org/10.1515/9783110302066
URL:
http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110302066&searchTitles=true
URL:
Volltext
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