Dynamic Motion Chaotic And Stochastic Behaviour

We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas.

Authors: Le Gall, Jean-François
Provides a concise and rigorous presentation of stochastic integration and stochastic calculus for continuous semimartingales
Presents major applications of stochastic calculus to Brownian motion and related stochastic processes
Includes important aspects of Markov processes with applications to stochastic differential equations and to connections with partial differential equations

This book is a complete treatise on the theory of nonlinear dynamics of chaotic and stochastic systems. It contains both an exhaustive introduction to the subject as well as a detailed discussion of fundamental problems and research results in a field to which the authors have made important contributions themselves. Despite the unified presentation of the subject, care has been taken to present the material in largely self-contained chapters.

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter.

This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance.

Many optimization questions arise in economics and finance; an important example of this is the society's choice of the optimum state of the economy (the social choice problem). Optimization in Economics and Finance extends and improves the usual optimization techniques, in a form that may be adopted for modeling social choice problems. Problems discussed include: when is an optimum reached; when is it unique; relaxation of the conventional convex (or concave) assumptions on an economic model; associated mathematical concepts such as invex and quasimax; multiobjective optimal control models; and related computational methods and programs. These techniques are applied to economic growth models (including small stochastic perturbations), finance and financial investment models (and the interaction between financial and production variables), modeling sustainability over long time horizons, boundary (transversality) conditions, and models with several conflicting objectives.