الصفحة 1
الصفحة 1
Non-negative Matrices and Markov Chains
This book is a photographic reproduction of the book of the same title published in 1981, for which there has been continuing demand on account of its accessible technical level. Its appearance also helped generate considerable subsequent work on inhomogeneous products of matrices. This printing adds an additional bibliography on coefficients of ergodicity and a list of corrigenda.
New Algorithms for Macromolecular Simulation
Molecular simulation is a widely used tool in biology, chemistry, physics and engineering. This book contains a collection of articles by leading researchers who are developing new methods for molecular modelling and simulation. Topics addressed here include: multiscale formulations for biomolecular modelling, such as quantum-classical methods and advanced solvation techniques; protein folding methods and schemes for sampling complex landscapes; membrane simulations; free energy calculation; and techniques for improving ergodicity. The book is meant to be useful for practitioners in the simulation community and for those new to molecular simulation who require a broad introduction to the state of the art.
Invariant Probabilities of Markov-Feller Operators and Their Supports
In this book invariant probabilities for a large class of discrete-time homogeneous Markov processes known as Feller processes are discussed. These Feller processes appear in the study of iterated function systems with probabilities, convolution operators, certain time series, etc. Rather than dealing with the processes, the transition probabilities and the operators associated with these processes are studied.
Interest Rate Models : an Infinite Dimensional Stochastic Analysis Perspective
Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective studies the mathematical issues that arise in modeling the interest rate term structure. These issues are approached by casting the interest rate models as stochastic evolution equations in infinite dimensions. The book is comprised of three parts. Part I is a crash course on interest rates, including a statistical analysis of the data and an introduction to some popular interest rate models. Part II is a self-contained introduction to infinite dimensional stochastic analysis, including SDE in Hilbert spaces and Malliavin calculus. Part III presents some recent results in interest rate theory, including finite dimensional realizations of HJM models, generalized bond portfolios, and the ergodicity of HJM models.
Ergodic Dynamics : From Basic Theory to Applications
This textbook provides a broad introduction to the fields of dynamical systems and ergodic theory. Motivated by examples throughout, the author offers readers an approachable entry-point to the dynamics of ergodic systems. Modern and classical applications complement the theory on topics ranging from financial fraud to virus dynamics, offering numerous avenues for further inquiry. Starting with several simple examples of dynamical systems, the book begins by establishing the basics of measurable dynamical systems, attractors, and the ergodic theorems. From here, chapters are modular and can be selected according to interest. Highlights include the Perron–Frobenius theorem, which is presented with proof and applications that include Google PageRank. An in-depth exploration of invariant measures includes ratio sets and type III measurable dynamical systems using the von Neumann factor classification. Topological and measure theoretic entropy are illustrated and compared in detail, with an algorithmic application of entropy used to study the papillomavirus genome. A chapter on complex dynamics introduces Julia sets and proves their ergodicity for certain maps. Cellular automata are explored as a series of case studies in one and two dimensions, including Conway’s Game of Life and latent infections of HIV. Other chapters discuss mixing properties, shift spaces, and toral automorphisms.
Eigenvalues, Inequalities, and Ergodic Theory
A problem of broad interest – the estimation of the spectral gap for matrices or differential operators (Markov chains or diffusions) – is covered in this book. The area has a wide range of applications, and provides a tool to describe the phase transitions and the effectiveness of random algorithms. In particular, the book studies a subset of the general problem, taking some approaches that have, up till now, only appeared largely in the Chinese literature.Eigenvalues, Inequalities and Ergodic Theory serves as an introduction to this developing field, and provides an overview of the methods used, in an accessible and concise manner.
Dependence in Probability and Statistics
This book gives a detailed account of some recent developments in the field of probability and statistics for dependent data. The book covers a wide range of topics from Markov chain theory and weak dependence with an emphasis on some recent developments on dynamical systems, to strong dependence in times series and random fields. A special section is devoted to statistical estimation problems and specific applications. The book is written as a succession of papers by some specialists of the field, alternating general surveys, mostly at a level accessible to graduate students in probability and statistics, and more general research papers mainly suitable to researchers in the field. The first part of the book considers some recent developments on weak dependent time series, including some new results for Markov chains as well as some developments on new notions of weak dependence. This part also intends to fill a gap between the probability and statistical literature and the dynamical system literature. The second part presents some new results on strong dependence with a special emphasis on non-linear processes and random fields currently encountered in applications. Finally, in the last part, some general estimation problems are investigated, ranging from rate of convergence of maximum likelihood estimators to efficient estimation in parametric or non-parametric time series models, with an emphasis on applications with non-stationary data.
An Introduction to Infinite-Dimensional Analysis
In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic functional analysis and measure theory but not necessarily probability theory – to analysis in a separable Hilbert space of infinite dimension.Starting from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate some basic stochastic dynamical systems (including dissipative nonlinearities) and Markov semi-groups, paying special attention to their long-time behavior: ergodicity, invariant measure. Here fundamental results like the theorems of Prokhorov, Von Neumann, Krylov-Bogoliubov and Khas'minski are proved. The last chapter is devoted to gradient systems and their asymptotic behavior.
