Measure-Valued Branching Markov Processes by Zenghu Li
This book provides a compact introduction to the theory of measure-valued branching processes, immigration processes and Ornstein–Uhlenbeck type processes.
Measure-valued branching processes arise as high density limits of branching particle systems. The first part of the book gives an analytic construction of a special class of such processes, the Dawson–Watanabe superprocesses, which includes the finite-dimensional continuous-state branching process as an example. Under natural assumptions, it is shown that the superprocesses have Borel right realizations. Transformations are then used to derive the existence and regularity of several different forms of the superprocesses. This technique simplifies the constructions and gives useful new perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The second part investigates immigration structures associated with the measure-valued branching processes. The structures are formulated by skewconvolution semigroups, which are characterized in terms of infinitely divisible probability entrance laws. A theory of stochastic equations for one-dimensional continuous-state branching processes with or without immigration is developed, which plays a key role in the construction of measure flows of those processes. The third part of the book studies a class of Ornstein-Uhlenbeck type processes in Hilbert spaces defined by generalized Mehler semigroups, which arise naturally in fluctuation limit theorems of the immigration superprocesses.
This volume is aimed at researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.
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Foundations of Modern Probability
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Geometry of Level Sets of Random Fields, Kac–Rice Formulas, Hermite Expansions and Applications
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Dynamics on Graphs
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Hybrid Switching Diffusions
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Nonlinear Expectations and Stochastic Calculus under Uncertainty
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Probability on Compact Lie Groups
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Pseudo-Regularly Varying Functions and Generalized Renewal Processes
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Stochastic Disorder Problems
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Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes
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Analysis and Approximation of Rare Events
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Random Ordinary Differential Equations and Their Numerical Solution
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Stochastic Evolution Systems
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Ambit Stochastics
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Mathematical Control Theory for Stochastic Partial Differential Equations
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Dirichlet Forms Methods for Poisson Point Measures and Levy Processes
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Lectures on Monte Carlo Theory
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Stochastic Control Theory
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Random Measures, Theory and Applications
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Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications
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Random Walks in the Quarter Plane
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Stochastic Flows and Jump-Diffusions
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Stochastic Multi-Stage Optimization
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The Quasispecies Equation and Classical Population Models
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Asymptotic Theory of Weakly Dependent Random Processes
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Stable Convergence and Stable Limit Theorems
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Stochastic Integration in Banach Spaces
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Continuous-Time Markov Decision Processes
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Dynamic Markov Bridges and Market Microstructure
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Limit Theorems for Multi-Indexed Sums of Random Variables
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Markov Renewal and Piecewise Deterministic Processes
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Convex Stochastic Optimization
| SKU | Unavailable |
| ISBN 13 | 9783662669099 |
| ISBN 10 | 3662669099 |
| Title | Measure-Valued Branching Markov Processes |
| Author | Zenghu Li |
| Series | Probability Theory And Stochastic Modelling |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Springer |
| Year published | 2023-03-14 |
| Number of pages | 475 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |