دانلود کتاب Dirichlet Forms and Symmetric Markov Processes

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Preface to the first and second edition\nPreface to the second edition\nContents\nNotation\nI Dirichlet Forms\n 1 Basic theory of Dirichlet forms\n 1.1 Basic notions\n 1.2 Examples\n 1.3 Closed forms and semigroups\n 1.4 Dirichlet forms and Markovian semigroups\n 1.5 Transience of Dirichlet spaces and extended Dirichlet spaces\n 1.6 Global properties of Markovian semigroups\n 2 Potential theory for Dirichlet forms\n 2.1 Capacity and quasi continuity\n 2.2 Measures of finite energy integrals\n 2.3 Reduced functions and spectral synthesis\n 2.4 Capacities and Sobolev type inequalities\n 3 The scope of Dirichlet forms\n 3.1 Closability and the smallest closed extensions\n 3.2 Formulae of Beurling–Deny and LeJan\n 3.3 Maximum Markovian extensions\nII Symmetric Markov processes\n 4 Analysis by symmetric Hunt processes\n 4.1 Smallness of sets and symmetry\n 4.2 Identification of potential theoretic notions\n 4.3 Orthogonal projections and hitting distributions\n 4.4 Parts of forms and processes\n 4.5 Continuity, killing, and jumps of sample paths\n 4.6 Quasi notions, fine notions and global properties\n 4.7 Irreducible recurrence and ergodicity\n 4.8 Recurrence and Poincaré type inequalities\n 5 Stochastic analysis by additive functionals\n 5.1 Positive continuous additive functionals and smooth measures\n 5.2 Decomposition of additive functionals of finite energy\n 5.3 Martingale additive functionals and Beurling–Deny formulae\n 5.4 Continuous additive functionals of zero energy\n 5.5 Extensions to additive functionals locally of finite energy\n 5.6 Martingale additive functionals of finite energy and stochastic integrals\n 5.7 Forward and backward martingale additive functionals\n 6 Transformations of forms and processes\n 6.1 Perturbed Dirichlet forms and killing by additive functionals\n 6.2 Traces of Dirichlet forms and time changes by additive functionals\n 6.2.1 Transient case\n 6.2.2 General case\n 6.3 Transformations by supermartingale multiplicative functionals\n 6.4 Donsker–Varadhan type large deviation principle\n 7 Construction of symmetric Markov processes\n 7.1 Construction of a Markovian transition function\n 7.2 Construction of a symmetric Hunt process\nAppendix\n A.1 Choquet capacities\n A.2 An introduction to Hunt processes\n A.3 A summary on martingale additive functionals\n A.4 Regular representations of Dirichlet spaces\n A.5 Solutions to Exercises\nNotes\nBibliography\nIndex