This book provides a comprehensive up-to-date presentation of some of the classical areas of reliability, based on a more advanced probabilistic framework using the modern theory of stochastic processes. This framework allows analysts to formulate general failure models, establish formulae for computing various performance measures, as well as determine how to identify optimal replacement policies in complex situations.
In this second edition of the book, two major topics have been added to the original version: copula models which are used to study the effect of structural...
This book provides a comprehensive up-to-date presentation of some of the classical areas of reliability, based on a more advanced probabilistic fr...
In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners' aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their...
In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computer...
Following the publication of the Japanese edition of this book, several inter- esting developments took place in the area. The author wanted to describe some of these, as well as to offer suggestions concerning future problems which he hoped would stimulate readers working in this field. For these reasons, Chapter 8 was added. Apart from the additional chapter and a few minor changes made by the author, this translation closely follows the text of the original Japanese edition. We would like to thank Professor J. L. Doob for his helpful comments on the English edition. T. Hida T. P. Speed v...
Following the publication of the Japanese edition of this book, several inter- esting developments took place in the area. The author wanted to descri...
Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. During that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in W onham 76J). At the same time, Girsanov 25J and Howard 26J made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier 4J. Two types of engineering problems engendered two different parts of stochastic control...
Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 19...
The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva- lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par- ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate." The...
The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual ...
The basis for this book is a number of lectures given frequently by the author to third year students of the Department of Economics at Leningrad State University who specialize in economical cybernetics. The main purpose of this book is to provide the student with a relatively simple and easy-to-understand manual containing the basic mathematical machinery utilized in the theory of games. Practical examples (including those from the field of economics) serve mainly as an interpretation of the mathematical foundations of this theory rather than as indications of their actual or potential...
The basis for this book is a number of lectures given frequently by the author to third year students of the Department of Economics at Leningrad Stat...
This book may be regarded as consisting of two parts. In Chapters I-IV we pre- sent what we regard as essential topics in an introduction to deterministic optimal control theory. This material has been used by the authors for one semester graduate-level courses at Brown University and the University of Kentucky. The simplest problem in calculus of variations is taken as the point of departure, in Chapter I. Chapters II, III, and IV deal with necessary conditions for an opti- mum, existence and regularity theorems for optimal controls, and the method of dynamic programming. The beginning...
This book may be regarded as consisting of two parts. In Chapters I-IV we pre- sent what we regard as essential topics in an introduction to determini...
Devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes, the text is mainly confined to MCPs with Borel state and control spaces. Although the book follows on from the author's earlier work, an important feature of this volume is that it is self-contained and can thus be read independently of the first. The control model studied is sufficiently general to include virtually all the usual discrete-time stochastic control models that appear in applications to engineering, economics, mathematical population processes, operations...
Devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes, the text is mainly confined to...
This book presents the first part of a planned two-volume series devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes (MCPs). Interest is mainly confined to MCPs with Borel state and control (or action) spaces, and possibly unbounded costs and noncompact control constraint sets. MCPs are a class of stochastic control problems, also known as Markov decision processes, controlled Markov processes, or stochastic dynamic pro- grams; sometimes, particularly when the state space is a countable set, they are also called Markov...
This book presents the first part of a planned two-volume series devoted to a systematic exposition of some recent developments in the theory of discr...
In wntmg this monograph my aim has been to present a "geometric" approach to the structural synthesis of multivariable control systems that are linear, time-invariant and of finite dynamic order. The book is ad- dressed to graduate students specializing in control, to engineering scientists involved in control systems research and development, and to mathemati- cians interested in systems control theory. The label "geometric" in the title is applied for several reasons. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract (geometric)...
In wntmg this monograph my aim has been to present a "geometric" approach to the structural synthesis of multivariable control systems that are linear...
