John G. Kemeny

Bio: John G. Kemeny is an academic researcher from Dartmouth College. The author has contributed to research in topics: Markov chain & Examples of Markov chains. The author has an hindex of 25, co-authored 85 publications receiving 8637 citations. Previous affiliations of John G. Kemeny include Princeton University.

Finite Markov chains

Abstract: Markov chains are one of the most useful classes of stochastic processes, being • simple, flexible and supported by many elegant theoretical results • valuable for building intuition about random dynamic models • central to quantitative modeling in their own right You will find them in many of the workhorse models of economics and finance. In this lecture we review some of the theory of Markov chains. We will also introduce some of the high quality routines for working with Markov chains available in QuantEcon.jl. Prerequisite knowledge is basic probability and linear algebra.

Finite Markov Chains.

Abstract: Markov chains are one of the most useful classes of stochastic processes, being • simple, flexible and supported by many elegant theoretical results • valuable for building intuition about random dynamic models • central to quantitative modeling in their own right You will find them in many of the workhorse models of economics and finance. In this lecture we review some of the theory of Markov chains. We will also introduce some of the high quality routines for working with Markov chains available in QuantEcon.jl. Prerequisite knowledge is basic probability and linear algebra.

Denumerable Markov chains

Abstract: This textbook provides a systematic treatment of denumerable Markov chains, covering both the foundations of the subject and topics in potential theory and boundary theory. It is a discussion of relations among what might be called the descriptive quantities associated with Markov chains - probabilities of events and means of random variables that give insight into the behaviour of the chains. The approach, by means of infinite matrices, simplifies the notation, shortens statements and proofs of theorems, and often suggests new results. This second edition includes a new chapter, "Introduction to Random Fields", written by David Giffeath.

Mathematical models in the social sciences

Abstract: As the need for more substantial mathematical training has increased among social science students, the lack of any adequate textbook between the very elementary and the very advanced levels has become crutial. The authors, long-time experts in this field, have answered the need with this volume, and the MIT Press has repsonded by bringing it into renewed circulation.Mathematical Models in the Social Sciences investigates and teaches the formation and analysis of mathematical models with detailed interpretations of the results. These models are self-contained, with the necessary mathematics included in each chapter. A vast range of topics in the social sciences and a wide variety of mathematical techniques are covered by the models. Ample opportunity is also provided for the students to form their own models. Republication of this book provides social science and mathematics students with a text that is the analogue of mathematical methods textbooks used in the study of the physical sciences and engineering. Prerequisites are kept to a minimum; a course in finite mathematics and a semester of calculus are all that is necessary.The chapters cover these main topics (and employ the mathematical approach parenthetically indicated): methodology; preference rankings (an axiomatic approach); ecology (two dynamic models); market stability (a dynamic model); a Markov chain model in sociology; stabilization of money flow (an application of discrete potential theory); branching processes; organization theory (applications of graph theory); and optimal scheduling (a problem in dynamic programming).

Pattern Recognition with Fuzzy Objective Function Algorithms

Abstract: New updated! The latest book from a very famous author finally comes out. Book of pattern recognition with fuzzy objective function algorithms, as an amazing reference becomes what you need to get. What's for is this book? Are you still thinking for what the book is? Well, this is what you probably will get. You should have made proper choices for your better life. Book, as a source that may involve the facts, opinion, literature, religion, and many others are the great friends to join with.

Simple mathematical models with very complicated dynamics

Abstract: First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.

Principles of Model Checking

Abstract: Our growing dependence on increasingly complex computer and software systems necessitates the development of formalisms, techniques, and tools for assessing functional properties of these systems. One such technique that has emerged in the last twenty years is model checking, which systematically (and automatically) checks whether a model of a given system satisfies a desired property such as deadlock freedom, invariants, and request-response properties. This automated technique for verification and debugging has developed into a mature and widely used approach with many applications. Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field. The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics LTL and CTL, compares them, and covers algorithms for verifying these logics, discussing real-time systems as well as systems subject to random phenomena. Separate chapters treat such efficiency-improving techniques as abstraction and symbolic manipulation. The book includes an extensive set of examples (most of which run through several chapters) and a complete set of basic results accompanied by detailed proofs. Each chapter concludes with a summary, bibliographic notes, and an extensive list of exercises of both practical and theoretical nature.

Learning to Predict by the Methods of Temporal Differences

Abstract: This article introduces a class of incremental learning procedures specialized for prediction – that is, for using past experience with an incompletely known system to predict its future behavior. Whereas conventional prediction-learning methods assign credit by means of the difference between predicted and actual outcomes, the new methods assign credit by means of the difference between temporally successive predictions. Although such temporal-difference methods have been used in Samuel's checker player, Holland's bucket brigade, and the author's Adaptive Heuristic Critic, they have remained poorly understood. Here we prove their convergence and optimality for special cases and relate them to supervised-learning methods. For most real-world prediction problems, temporal-difference methods require less memory and less peak computation than conventional methods and they produce more accurate predictions. We argue that most problems to which supervised learning is currently applied are really prediction problems of the sort to which temporal-difference methods can be applied to advantage.

Foundations of modern probability

Abstract: * Measure Theory-Basic Notions * Measure Theory-Key Results * Processes, Distributions, and Independence * Random Sequences, Series, and Averages * Characteristic Functions and Classical Limit Theorems * Conditioning and Disintegration * Martingales and Optional Times * Markov Processes and Discrete-Time Chains * Random Walks and Renewal Theory * Stationary Processes and Ergodic Theory * Special Notions of Symmetry and Invariance * Poisson and Pure Jump-Type Markov Processes * Gaussian Processes and Brownian Motion * Skorohod Embedding and Invariance Principles * Independent Increments and Infinite Divisibility * Convergence of Random Processes, Measures, and Sets * Stochastic Integrals and Quadratic Variation * Continuous Martingales and Brownian Motion * Feller Processes and Semigroups * Ergodic Properties of Markov Processes * Stochastic Differential Equations and Martingale Problems * Local Time, Excursions, and Additive Functionals * One-Dimensional SDEs and Diffusions * Connections with PDEs and Potential Theory * Predictability, Compensation, and Excessive Functions * Semimartingales and General Stochastic Integration * Large Deviations * Appendix 1: Advanced Measure Theory * Appendix 2: Some Special Spaces * Historical and Bibliographical Notes * Bibliography * Indices