Presents the theory of general irreducible Markov chains and its connection to the Perron-Frobenius theory of nonnegative operators.

Non-Homogeneous Markov Chains and Systems: Theory and Applications fulfills two principal goals. It is devoted to the study of non-homogeneous Markov chains in the first part, and to the evolution of the theory and applications of non-homogeneous Markov systems (populations) in the second. The book is self-contained, requiring a moderate background in basic probability theory and linear algebra, common to most undergraduate programs in mathematics, statistics, and applied probability. There are some advanced parts, which need measure theory and other advanced mathematics, but the readers are alerted to these so they may focus on the basic results. Features A broad and accessible overview of non-homogeneous Markov chains and systems Fills a significant gap in the current literature A good balance of theory and applications, with advanced mathematical details separated from the main results Many illustrative examples of potential applications from a variety of fields Suitable for use as a course text for postgraduate students of applied probability, or for self-study Potential applications included could lead to other quantitative areas The book is primarily aimed at postgraduate students, researchers, and practitioners in applied probability and statistics, and the presentation has been planned and structured in a way to provide flexibility in topic selection so that the text can be adapted to meet the demands of different course outlines. The text could be used to teach a course to students studying applied probability at a postgraduate level or for self-study. It includes many illustrative examples of potential applications, in order to be useful to researchers from a variety of fields.

This book is representative of the work of Chinese probabilists on probability theory and its applications in physics. It presents a unique treatment of general Markov jump processes: uniqueness, various types of ergodicity, Markovian couplings, reversibility, spectral gap, etc. It also deals with a typical class of non-equilibrium particle systems, including the typical Schlögl model taken from statistical physics. The constructions, ergodicity and phase transitions for this class of Markov interacting particle systems, namely, reaction-diffusion processes, are presented. In this new edition, a large part of the text has been updated and two-and-a-half chapters have been rewritten. The book is self-contained and can be used in a course on stochastic processes for graduate students.

This monograph presents a new approach to the investigation of ergodicity and stability problems for homogeneous Markov chains with a discrete-time and with values in a measurable space. The main purpose of this book is to highlight various methods for the explicit evaluation of estimates for convergence rates in ergodic theorems and in stability theorems for wide classes of chains. These methods are based on the classical perturbation theory of linear operators in Banach spaces and give new results even for finite chains. In the first part of the book, the theory of uniform ergodic chains with respect to a given norm is developed. In the second part of the book the condition of the uniform ergodicity is removed.

Stochastic geometry involves the study of random geometric structures, and blends geometric, probabilistic, and statistical methods to provide powerful techniques for modeling and analysis. Recent developments in computational statistical analysis, particularly Markov chain Monte Carlo, have enormously extended the range of feasible applications. Stochastic Geometry: Likelihood and Computation provides a coordinated collection of chapters on important aspects of the rapidly developing field of stochastic geometry, including: o a "crash-course" introduction to key stochastic geometry themes o considerations of geometric sampling bias issues o tesselations o shape o random sets o image analysis o spectacular advances in likelihood-based inference now available to stochastic geometry through the techniques of Markov chain Monte Carlo

New up-to-date edition of this influential classic on Markov chains in general state spaces. Proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background. New commentary by Sean Meyn, including updated references, reflects developments since 1996.

Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems.

Advanced Methods of Pharmacokinetic and Pharmocodynamic Systems Analysis Volume 3 is vital to professionals and academicians working in drug development and bioengineering. Both basic and clinical scientists will benefit from this work. This book contains chapters by leading researchers in pharmacokinetic/pharmacodynamic modeling and will be of interest to anyone involved with the application of pharmacokinetic and pharmacodynamics to drug development. The use of mathematical modeling and associated computational methods is central to the study of the absorption, distribution and elimination of therapeutic drugs (pharmacokinetics) and to understanding how drugs produce their effects (pharmacodynamics). From its inception, the field of pharmacokinetics and pharmacodynamics has incorporated methods of mathematical modeling, simulation and computation in an effort to better understand and quantify the processes of uptake, disposition and action of therapeutic drugs. These methods for pharmacokinetic/pharmacodynamic systems analysis impact all aspects of drug development. In vitro, animal and human testing, as well as drug therapy are all influenced by these methods. Modeling methodologies developed for studying pharmacokinetic/ pharmacodynamic processes confront many challenges. This is related in part to the severe restrictions on the number and type of measurements that are available from laboratory experiments and clinical trials, as well as the variability in the experiments and the uncertainty associated with the processes themselves. The contributions are organized in three main areas: Mechanism-Based PK/PD, Pharmacometrics and Pharmacotherapy. Both professionals and academics will profit from this extensive work.

We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.