Markov Processes: Characterisation and Convergence (Probability & Mathematical Statistics)

Reseña del editor:

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 L 1 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 L 2 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.

Nota de la solapa:

The recognition that each method for verifying weak convergence is closely tied to a method for characterizing the limiting process Sparked this broad study of characterization and convergence problems for Markov processes. A number of topics are presented for the first time in book form, such as Martingale problems for general Markov processes, powerful criteria for convergence in distribution in DE[O,???), multiple random time transformations, duality as a method of characterizing Markov processes, and characterizations of stationary distributions. The authors illustrate several different approaches to proving weak approximation theoremsoperator semigroup convergence theorems, Martingale characterization of Markov processes, and representation of the processes as solutions of stochastic equations. The heart of the book reveals the main characterization and convergence results, with an emphasis on diffusion processes. Applications to branching and population processes, genetic models, and random evolutions, are given. Useful to the professional as a reference, 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.

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