XII Symposium of Probability and Stochastic Processes - Info and Reading Options

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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 -- 4.3 Self-Similar Fragmentation Trees -- 4.3.1 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 -- 6.3 Related Random Geometric Structures -- References -- 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 -- 2.2 Scale Functions

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