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  • 1
    Online Resource
    Online Resource
    Berlin : De Gruyter
    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. , 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. , 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
    URL: Volltext  (lizenzpflichtig)
    URL: Cover
    URL: Cover
    URL: Cover
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