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" XII Symposium of Probability and Stochastic Processes : "
Daniel Hernández-Hernández, Juan Carlos Pardo, Victor Rivero, editors.
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BL
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865464
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Symposium on Probability and Stochastic Processes(12th :2015 :, Mérida, Mexico)
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XII Symposium of Probability and Stochastic Processes : : Merida, Mexico, November 16--20, 2015 /\ Daniel Hernández-Hernández, Juan Carlos Pardo, Victor Rivero, editors.
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| Publication Statement
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Cham, Switzerland :: Birkhäuser,, 2018.
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| Series Statement
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Progress in probability ;; 73
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1 online resource
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| ISBN
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3319776436
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: 9783319776439
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9783319776422
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| Contents
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Intro; Introduction; Contents; Part I Courses; Scaling Limits of Markov-Branching Trees and Applications; 1 Introduction; 2 Discrete Trees, Examples and Motivations; 2.1 Discrete Trees; 2.2 First Examples; 2.3 The Markov-Branching Property; 3 The Example of Galton-Watson Trees and Topological Framework; 3.1 Real Trees and the Gromov-Hausdorff Topology; 3.2 Scaling Limits of Conditioned Galton-Watson Trees; 4 Scaling Limits of Markov-Branching Trees; 4.1 A Markov Chain in the Markov-Branching Sequence of Trees; 4.2 Scaling Limits of Non-increasing Markov Chains
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2.2 Scale Functions2.3 Smoothness of Scale Functions; 2.4 Fluctuation Identities for Spectrally Negative Lévy Processes; 2.4.1 Two-Sided Exit; 2.4.2 Resolvent Measures; 2.5 Fluctuation Identities for the Infimum and Reflected Processes; 2.5.1 Fluctuation Identities for the Infimum Process; 2.5.2 Fluctuation Identities for tb; 2.5.3 Fluctuation Identities for Yta; 2.6 Fluctuation Identities for Doubly Reflected Lévy Processes; 2.7 Other Properties of the Scale Function; 2.7.1 Asymptotics as x →∞; 2.7.2 Log-Concavity; 2.7.3 Martingale Properties; 2.8 Some Further Notations
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3 Two-Sided Singular Control3.1 The Double Reflection Strategy; 3.2 Smoothness of the Value Function; 3.3 Existence of (a*, b*); 3.3.1 The Case of Example 3.1; 3.3.2 The Case of Example 3.2; 3.3.3 The Case of Example 3.3; 3.4 Variational Inequalities and Verification; 4 Impulse Control; 4.1 The (s, S)-Strategy; 4.2 Smoothness of the Value Function; 4.2.1 The Case of Example 4.3; 4.2.2 Brief Remarks on the Cases of Examples 4.1 and 4.2; 4.3 Quasi-Variational Inequalities and Verification; 4.3.1 The Case of Example 4.3; 4.3.2 Brief Remarks on the Cases of Examples 4.1 and 4.2
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4.3 Self-Similar Fragmentation Trees4.3.1 Self-Similar Fragmentation Processes; 4.3.2 Self-Similar Fragmentation Trees; 4.4 Scaling Limits of Markov-Branching Trees; 5 Applications; 5.1 Galton-Watson Trees; 5.1.1 Galton-Watson Trees with n Vertices; 5.1.2 Galton-Watson Trees with Arbitrary Degree Constraints; 5.2 Pólya Trees; 5.3 Dynamical Models of Tree Growth; 5.3.1 Ford's Alpha Model; 5.3.2 k-Ary Growing Trees; 5.3.3 Marginals of Stable Trees; 5.4 Cut-Trees; 6 Further Perspectives; 6.1 Multi-Type Markov-Branching Trees and Applications; 6.2 Local Limits
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6.3 Related Random Geometric StructuresReferences; Optimality of Two-Parameter Strategies in Stochastic Control; 1 Introduction; 1.1 One-Parameter Strategies; 1.2 Two-Parameter Strategies; 1.2.1 Two-Sided Singular Control; 1.2.2 Impulse Control; 1.2.3 Zero-Sum Games Between Two Players; 1.3 Fluctuation Theory of Spectrally One-Sided Lévy Processes; 1.4 Solution Procedures; 1.4.1 Selection of the Two Parameters; 1.4.2 Verification of Optimality; 1.5 Comparison with Other Approaches; 1.6 Computation; 2 Spectrally Negative Lévy Processes and Scale Functions; 2.1 Path Variations and Regularity
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| Abstract
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This volume contains the proceedings of the XII Symposium of Probability and Stochastic Processes which took place at Universidad Autonoma de Yucatan in Merida, Mexico, on November 16-20, 2015. This meeting was the twelfth meeting in a series of ongoing biannual meetings aimed at showcasing the research of Mexican probabilists as well as promote new collaborations between the participants. The book features articles drawn from different research areas in probability and stochastic processes, such as: risk theory, limit theorems, stochastic partial differential equations, random trees, stochastic differential games, stochastic control, and coalescence. Two of the main manuscripts survey recent developments on stochastic control and scaling limits of Markov-branching trees, written by Kazutoshi Yamasaki and Bénédicte Haas, respectively. The research-oriented manuscripts provide new advances in active research fields in Mexico. The wide selection of topics makes the book accessible to advanced graduate students and researchers in probability and stochastic processes.
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Probabilities, Congresses.
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Stochastic processes, Congresses.
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Calculus of variations.
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Cybernetics systems theory.
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Differential calculus equations.
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Game theory.
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MATHEMATICS-- Applied.
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MATHEMATICS-- Probability Statistics-- General.
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Probabilities.
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Probability statistics.
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Stochastic processes.
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| Dewey Classification
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519.2
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| LC Classification
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QA273.A1
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| Added Entry
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Hernández-Hernández, Daniel
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Pardo, Juan Carlos
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Rivero, Victor
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