The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions
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The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions
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Author : Christian Soize
language : en
Publisher: World Scientific
Release Date : 1994-05-16
The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions written by Christian Soize and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-05-16 with Mathematics categories.
This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method.The author answers three types of questions concerning this area. First, what probabilistic tools are necessary for constructing a stochastic model and deriving the FKP equation for nonlinear stochastic dynamical systems? Secondly, what are the main results concerning the existence and uniqueness of an invariant measure and its associated stationary response? Finally, what is the class of multidimensional dynamical systems that have an explicit invariant measure and what are the fundamental examples for applications?
The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions
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Author : Christian Soize
language : en
Publisher: World Scientific
Release Date : 1994
The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions written by Christian Soize and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.
This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method.The author answers three types of questions concerning this area. First, what probabilistic tools are necessary for constructing a stochastic model and deriving the FKP equation for nonlinear stochastic dynamical systems? Secondly, what are the main results concerning the existence and uniqueness of an invariant measure and its associated stationary response? Finally, what is the class of multidimensional dynamical systems that have an explicit invariant measure and what are the fundamental examples for applications?
Asymptotic Methods For The Fokker Planck Equation And The Exit Problem In Applications
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Author : Johan Grasman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Asymptotic Methods For The Fokker Planck Equation And The Exit Problem In Applications written by Johan Grasman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.
Impulsive Differential Equations
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Author : Dimit?r Ba?nov
language : en
Publisher: World Scientific
Release Date : 1995
Impulsive Differential Equations written by Dimit?r Ba?nov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.
Introduction To Stochastic Calculus With Applications 3rd Edition
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Author : Fima C Klebaner
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-03-21
Introduction To Stochastic Calculus With Applications 3rd Edition written by Fima C Klebaner and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-21 with Mathematics categories.
This book presents a concise and rigorous treatment of stochastic calculus. It also gives its main applications in finance, biology and engineering. In finance, the stochastic calculus is applied to pricing options by no arbitrage. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. Not everything is proved, but enough proofs are given to make it a mathematically rigorous exposition.This book aims to present the theory of stochastic calculus and its applications to an audience which possesses only a basic knowledge of calculus and probability. It may be used as a textbook by graduate and advanced undergraduate students in stochastic processes, financial mathematics and engineering. It is also suitable for researchers to gain working knowledge of the subject. It contains many solved examples and exercises making it suitable for self study.In the book many of the concepts are introduced through worked-out examples, eventually leading to a complete, rigorous statement of the general result, and either a complete proof, a partial proof or a reference. Using such structure, the text will provide a mathematically literate reader with rapid introduction to the subject and its advanced applications. The book covers models in mathematical finance, biology and engineering. For mathematicians, this book can be used as a first text on stochastic calculus or as a companion to more rigorous texts by a way of examples and exercises./a
Stability And Time Optimal Control Of Hereditary Systems With Application To The Economic Dynamics Of The Us 2nd Edition
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Author : Ethelbert Nwakuche Chukwu
language : en
Publisher: World Scientific Publishing Company
Release Date : 2001-12-28
Stability And Time Optimal Control Of Hereditary Systems With Application To The Economic Dynamics Of The Us 2nd Edition written by Ethelbert Nwakuche Chukwu and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-28 with Mathematics categories.
Stability and Time-Optimal Control of Hereditary Systems is the mathematical foundation and theory required for studying in depth the stability and optimal control of systems whose history is taken into account. In this edition, the economic application is enlarged, and explored in some depth. The application holds out the hope that full employment and high income growth will be compatible with low prices and low inflation, provided that the control matrix has full rank, i.e., the existing controls are fully effectively used. The book concludes with a new appendix containing complete programs, data, graphs and quantitative results for the US economy.
Differential Models And Neutral Systems For Controlling The Wealth Of Nations
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Author : Ethelbert N. Chukwu
language : en
Publisher: World Scientific
Release Date : 2001
Differential Models And Neutral Systems For Controlling The Wealth Of Nations written by Ethelbert N. Chukwu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Business & Economics categories.
This monograph derives from familiar economic principles the dynamics of national income, the interest rate, employment, the value of capital stock, prices, and the cumulative balance of payments. This is a Volterra neutral integrodifferential game of pursuit. The quarry control is government intervention in the form of taxation, control of money supply, tariffs, foreign credit, interest equalization tax, preferential trade agreements (which reduce trade barriers and enhance trade flows between nations), transportation and distance between trading partners. The pursuer controls include wages and productivity. The book provides conditions for controllability and then deduces how big government intervention (compared with private firms' contributions) should be to ensure the possibility of growth.The reader is assumed to be familiar with advanced calculus and to have a working knowledge of ordinary differential equations. The required theory of hereditary systems can be obtained from the book itself.
Mechanical And Thermodynamical Modeling Of Fluid Interfaces
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Author : Rene Gatignol
language : en
Publisher: World Scientific
Release Date : 2001
Mechanical And Thermodynamical Modeling Of Fluid Interfaces written by Rene Gatignol and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This book constitutes a comprehensive survey of the balance equations for mass, momentum and energy for the interfaces in pure fluids and mixtures. Constitutive laws are presented for many situations in engineering science, and examples are provided, including surface viscosity effects, variable surface tension and vapor recoil. In addition, some extensions of existing theory are given: stretch effect in premixed flames, relaxation zones downstream two-phase shock waves, and effective surface tension for high gradient zones.
Nondeterministic Mechanics
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Author : Isaac Elishakoff
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-30
Nondeterministic Mechanics written by Isaac Elishakoff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-30 with Technology & Engineering categories.
Table of contents: Stochastic methods in nonlinear structural dynamics.- Stochastic models of uncertainties in computational structural dynamics and structural acoustics.- The tale of stochastic linearization techniques: over half a century of progress.- Comprehensive modeling of uncertain systems using fuzzy set theory.- Bounding uncertainty in civil engineering: theoretical background and applications.- Combined methods in nondeterministic mechanics. In this book the current state of the art of nondeterministic mechanics in its various forms is presented. The topics range from stochastic problems to fuzzy sets; from linear to nonlinear problems; from specific methodologies to combinations of various techniques; from theoretical considerations to practical applications. It is specially designed to illuminate the various aspects of the three methodologies (probabilistic or stochastic modelling, fuzzy sets based analysis, antioptimization of structures) to deal with various uncertainties and deepen the discussion of their pros and cons.
Differential Equations Bifurcations And Chaos In Economics
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Author : Wei-bin Zhang
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-07-18
Differential Equations Bifurcations And Chaos In Economics written by Wei-bin Zhang and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-18 with Business & Economics categories.
Although the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics.