Jean B. Lasserre's Books

Markov Chains and Invariant Probabilities

By: Onésimo Hernández-Lerma,Jean B. Lasserre

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Markov Chains and Invariant Probabilities

By: Onésimo Hernández-Lerma,Jean B. Lasserre

This book is about discrete-time, time-homogeneous, Markov chains (Mes) and their ergodic behavior. To this end, most of the material is in fact about stable Mes, by which we mean Mes that admit an invariant probability measure. To state this more precisely and give an overview of the questions we shall be dealing with, we will first introduce some notation and terminology. Let (X,B) be a measurable space, and consider a X-valued Markov chain ~. = {~k' k = 0, 1, ... } with transition probability function (t.pJ.) P(x, B), i.e., P(x, B) := Prob (~k+1 E B I ~k = x) for each x E X, B E B, and k = 0,1, .... The Me ~. is said to be stable if there exists a probability measure (p.m.) /.l on B such that (*) VB EB. /.l(B) = Ix /.l(dx) P(x, B) If (*) holds then /.l is called an invariant p.m. for the Me ~. (or the t.p.f. P).

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Page Count

213

Publisher

Birkhäuser

Published Date

ISBN 10

3034880243

ISBN 13

9783034880244

Further Topics on Discrete-Time Markov Control Processes

By: Onesimo Hernandez-Lerma,Jean B. Lasserre

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Further Topics on Discrete-Time Markov Control Processes

By: Onesimo Hernandez-Lerma,Jean B. Lasserre

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 research, and management science.

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Page Count

286

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461205611

ISBN 13

9781461205616

Modern Optimization Modelling Techniques

By: Roberto Cominetti,Francisco Facchinei,Jean B. Lasserre

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Modern Optimization Modelling Techniques

By: Roberto Cominetti,Francisco Facchinei,Jean B. Lasserre

The theory of optimization, understood in a broad sense, is the basis of modern applied mathematics, covering a large spectrum of topics from theoretical considerations (structure, stability) to applied operational research and engineering applications. The compiled material of this book puts on display this versatility, by exhibiting the three parallel and complementary components of optimization: theory, algorithms, and practical problems. The book contains an expanded version of three series of lectures delivered by the authors at the CRM in July 2009. The first part is a self-contained course on the general moment problem and its relations with semidefinite programming. The second part is dedicated to the problem of determination of Nash equilibria from an algorithmic viewpoint. The last part presents congestion models for traffic networks and develops modern optimization techniques for finding traffic equilibria based on stochastic optimization and game theory.

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Page Count

265

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3034802919

ISBN 13

9783034802918

Discrete-Time Markov Control Processes

Basic Optimality Criteria

By: Onesimo Hernandez-Lerma,Jean B. Lasserre

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Discrete-Time Markov Control Processes

Basic Optimality Criteria

By: Onesimo Hernandez-Lerma,Jean B. Lasserre

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 decision (or controlled Markov) chains. Regardless of the name used, MCPs appear in many fields, for example, engineering, economics, operations research, statistics, renewable and nonrenewable re source management, (control of) epidemics, etc. However, most of the lit erature (say, at least 90%) is concentrated on MCPs for which (a) the state space is a countable set, and/or (b) the costs-per-stage are bounded, and/or (c) the control constraint sets are compact. But curiously enough, the most widely used control model in engineering and economics--namely the LQ (Linear system/Quadratic cost) model-satisfies none of these conditions. Moreover, when dealing with "partially observable" systems) a standard approach is to transform them into equivalent "completely observable" sys tems in a larger state space (in fact, a space of probability measures), which is uncountable even if the original state process is finite-valued.

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Page Count

223

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461207290

ISBN 13

9781461207290

Book's by Jean B. Lasserre

Markov Chains and Invariant Probabilities

Markov Chains and Invariant Probabilities

Further Topics on Discrete-Time Markov Control Processes

Further Topics on Discrete-Time Markov Control Processes

Modern Optimization Modelling Techniques

Modern Optimization Modelling Techniques

Discrete-Time Markov Control Processes

Discrete-Time Markov Control Processes

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