Synopses & Reviews
Recursive Estimation and Control for Stochastic Systems Han-Fu Chen This self-contained volume presents both the discrete-time and continuous-time systems, and incorporates not only well-known results in these fields but also many of the latest research findings. It shows how to analyze the convergence of recursive estimates through a combination of the probabilistic and ordinary differential equation methods and establishes the connection between the Gauss-Markov estimate and the Kalman filter through stochastic observability, and more. 1985 (0 471-81566-7) 378 pp. Nonparametric Density Estimation The L1 View Luc Devroye and Laszlo Gyorfi The first systematic, single-source examination that develops from first principles the " natural" theory for density estimation and shows why the classical L2 theory masks some fundamental properties of density estimates. Linking different subareas of statistics, including simulation, pattern recognition, detection theory, and minimax theory, it shows how to construct, use, and analyze density estimates. Relevant recent literature is tied in with the classical works of Parzen, Rosenblatt, and others. 1985 (0 471-81646-9) 368 pp. Elements of Applied Stochastic Processes Second Edition U. Narayan Bhat An applied introduction to stochastic models, this expanded and revised account develops basic concepts and techniques and applies them to problems arising in queueing, reliability, inventory and computer communications, social and behavioral processes, business management, and time series analysis. 1984 (0 471-87826-X) 736 pp.
Synopsis:
Converted into a paperback format, at a reduced price Markov Processes: Characterization and Convergence is ideal as a graduate text and/or reference on Markov Processes and their relationship to operator semigroups. This book presents several different approaches to proving weak approximation theorems for Markov processes, emphasizing the interplay of methods of characterization and approximation. Martingale problems for general Markov processes are systematically developed for the first time in book form. Concrete examples and an extensive bibliography are provided.
Synopsis:
Markov Processes presents several different approaches to proving weak approximation theorems for Markov processes, emphasizing the interplay of methods of characterization and approximation. Martingale problems for general Markov processes are systematically developed for the first time in book form. Useful to the professional as a reference and suitable for the graduate student as a text, this volume features a table of the interdependencies among the theorems, an extensive bibliography, and end-of-chapter problems.
About the Author
STEWART N. ETHIER, PhD, is Professor of Mathematics at the University of Utah. He received his PhD in mathematics at the University of Wisconsin–Madison.
THOMAS G. KURTZ, PhD, is Professor of Mathematics and Statistics at the University of Wisconsin–Madison. He is a Book Review Editor for The Annals of Probability and the author of Approximation of Population Processes. Dr. Kurtz obtained his PhD in mathematics at Stanford University.
Table of Contents
Introduction.
1. Operator Semigroups.
2. Stochastic Processes and Martingales.
3. Convergence of Probability Measures.
4. Generators and Markov Processes.
5. Stochastic Integral Equations.
6. Random Time Changes.
7. Invariance Principles and Diffusion Approximations.
8. Examples of Generators.
9. Branching Processes.
10. Genetic Models.
11. Density Dependent Population Processes.
12. Random Evolutions.
Appendixes.
References.
Index.
Flowchart.
Don't Miss
