Stochastic World

Author: Sergey S. Stepanov
Publisher: Springer Science & Business Media
ISBN: 3319000713
Format: PDF, ePub, Docs
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This book is an introduction into stochastic processes for physicists, biologists and financial analysts. Using an informal approach, all the necessary mathematical tools and techniques are covered, including the stochastic differential equations, mean values, probability distribution functions, stochastic integration and numerical modeling. Numerous examples of practical applications of the stochastic mathematics are considered in detail, ranging from physics to the financial theory. A reader with basic knowledge of the probability theory should have no difficulty in accessing the book content.

Advanced Mathematical Tools for Automatic Control Engineers Volume 2

Author: Alex Poznyak
Publisher: Elsevier
ISBN: 9780080914039
Format: PDF
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Advanced Mathematical Tools for Automatic Control Engineers, Volume 2: Stochastic Techniques provides comprehensive discussions on statistical tools for control engineers. The book is divided into four main parts. Part I discusses the fundamentals of probability theory, covering probability spaces, random variables, mathematical expectation, inequalities, and characteristic functions. Part II addresses discrete time processes, including the concepts of random sequences, martingales, and limit theorems. Part III covers continuous time stochastic processes, namely Markov processes, stochastic integrals, and stochastic differential equations. Part IV presents applications of stochastic techniques for dynamic models and filtering, prediction, and smoothing problems. It also discusses the stochastic approximation method and the robust stochastic maximum principle. Provides comprehensive theory of matrices, real, complex and functional analysis Provides practical examples of modern optimization methods that can be effectively used in variety of real-world applications Contains worked proofs of all theorems and propositions presented

Stochastic Calculus

Author: Mircea Grigoriu
Publisher: Springer Science & Business Media
ISBN: 9780817642426
Format: PDF
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"This self-contained text may be used for several graduate courses and as an important reference resource for applied scientists interested in analytical and numerical methods for solving stochastic problems."--BOOK JACKET.

Stochastic Methods for Estimation and Problem Solving in Engineering

Author: Kadry, Seifedine
Publisher: IGI Global
ISBN: 1522550461
Format: PDF, ePub
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Utilizing mathematical algorithms is an important aspect of recreating real-world problems in order to make important decisions. By generating a randomized algorithm that produces statistical patterns, it becomes easier to find solutions to countless situations. Stochastic Methods for Estimation and Problem Solving in Engineering provides emerging research on the role of random probability systems in mathematical models used in various fields of research. While highlighting topics, such as random probability distribution, linear systems, and transport profiling, this book explores the use and behavior of uncertain probability methods in business and science. This book is an important resource for engineers, researchers, students, professionals, and practitioners seeking current research on the challenges and opportunities of non-deterministic probability models.

Stochastic Differential Equations

Author: K. Sobczyk
Publisher: Springer Science & Business Media
ISBN: 9401137129
Format: PDF, ePub
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'Et moi, ..~ si lavait su CO.llUlJalt en revc:nir, One acMcc matbcmatica bu JaIdcred the human rac:c. It bu put COIDIDOD _ beet je n'y serais point aBe.' Jules Verne wbac it bdoup, 0Jl!be~ IbcII _t to!be dusty cauialcr Iabc & d 'diMardod__ The series is divergent; thc:reforc we may be -'. I!.ticT. Bc:I1 able to do something with it. O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world when: both feedback and non linearities abound. Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statcmalts as: 'One service topology has rendered mathematical physics ...-; 'One service logic has rendered c0m puter science ... '; 'One service category theory has rendered mathematics ... '. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. This series, Mathematics and Its Applications. started in 19n. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope. At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However. the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branc:hes. It also happens, quite often in fact, that branches which were thought to be completely.

Stochastic Global Optimization and Its Applications with Fuzzy Adaptive Simulated Annealing

Author: Hime Aguiar e Oliveira Junior
Publisher: Springer Science & Business Media
ISBN: 364227479X
Format: PDF, ePub, Mobi
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Stochastic global optimization is a very important subject, that has applications in virtually all areas of science and technology. Therefore there is nothing more opportune than writing a book about a successful and mature algorithm that turned out to be a good tool in solving difficult problems. Here we present some techniques for solving several problems by means of Fuzzy Adaptive Simulated Annealing (Fuzzy ASA), a fuzzy-controlled version of ASA, and by ASA itself. ASA is a sophisticated global optimization algorithm that is based upon ideas of the simulated annealing paradigm, coded in the C programming language and developed to statistically find the best global fit of a nonlinear constrained, non-convex cost function over a multi-dimensional space. By presenting detailed examples of its application we want to stimulate the reader’s intuition and make the use of Fuzzy ASA (or regular ASA) easier for everyone wishing to use these tools to solve problems. We kept formal mathematical requirements to a minimum and focused on continuous problems, although ASA is able to handle discrete optimization tasks as well. This book can be used by researchers and practitioners in engineering and industry, in courses on optimization for advanced undergraduate and graduate levels, and also for self-study.

Advanced Mathematics for Engineers with Applications in Stochastic Processes

Author: Aliakbar Montazer Haghighi
Publisher: Nova Science Pub Incorporated
ISBN: 9781608768806
Format: PDF
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Topics in advanced mathematics for engineers, probability and statistics typically span three subject areas, are addressed in three separate textbooks and taught in three different courses in as many as three semesters. Due to this arrangement, students taking these courses have had to shelf some important and fundamental engineering courses until much later than is necessary. This practice has generally ignored some striking relations that exist between the seemingly separate areas of statistical concepts, such as moments and estimation of Poisson distribution parameters. On one hand, these concepts commonly appear in stochastic processes -- for instance, in measures on effectiveness in queuing models. On the other hand, they can also be viewed as applied probability in engineering disciplines -- mechanical, chemical, and electrical, as well as in engineering technology. There is obviously, an urgent need for a textbook that recognises the corresponding relationships between the various areas and a matching cohesive course that will see through to their fundamental engineering courses as early as possible. This book is designed to achieve just that. Its seven chapters, while retaining their individual integrity, flow from selected topics in advanced mathematics such as complex analysis and wavelets to probability, statistics and stochastic processes.

Introduction to Stochastic Calculus with Applications

Author: Fima C Klebaner
Publisher: World Scientific Publishing Company
ISBN: 1911298674
Format: PDF, ePub
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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. Contents:Preliminaries From CalculusConcepts of Probability TheoryBasic Stochastic ProcessesBrownian Motion CalculusStochastic Differential EquationsDiffusion ProcessesMartingalesCalculus for SemimartingalesPure Jump ProcessesChange of Probability MeasureApplications in Finance: Stock and FX OptionsApplications in Finance: Bonds, Rates and OptionsApplications in BiologyApplications in Engineering and Physics Readership: Academics, mathematicians, advanced undergraduates, graduates, practitioners in finance, risk managers and electrical engineers.

Probability and Random Processes

Author: Venkatarama Krishnan
Publisher: John Wiley & Sons
ISBN: 0471998281
Format: PDF
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A resource for probability AND random processes, with hundreds ofworked examples and probability and Fourier transform tables This survival guide in probability and random processes eliminatesthe need to pore through several resources to find a certainformula or table. It offers a compendium of most distributionfunctions used by communication engineers, queuing theoryspecialists, signal processing engineers, biomedical engineers,physicists, and students. Key topics covered include: * Random variables and most of their frequently used discrete andcontinuous probability distribution functions * Moments, transformations, and convergences of randomvariables * Characteristic, generating, and moment-generating functions * Computer generation of random variates * Estimation theory and the associated orthogonalityprinciple * Linear vector spaces and matrix theory with vector and matrixdifferentiation concepts * Vector random variables * Random processes and stationarity concepts * Extensive classification of random processes * Random processes through linear systems and the associated Wienerand Kalman filters * Application of probability in single photon emission tomography(SPECT) More than 400 figures drawn to scale assist readers inunderstanding and applying theory. Many of these figures accompanythe more than 300 examples given to help readers visualize how tosolve the problem at hand. In many instances, worked examples aresolved with more than one approach to illustrate how differentprobability methodologies can work for the same problem. Several probability tables with accuracy up to nine decimal placesare provided in the appendices for quick reference. A specialfeature is the graphical presentation of the commonly occurringFourier transforms, where both time and frequency functions aredrawn to scale. This book is of particular value to undergraduate and graduatestudents in electrical, computer, and civil engineering, as well asstudents in physics and applied mathematics. Engineers, computerscientists, biostatisticians, and researchers in communicationswill also benefit from having a single resource to address mostissues in probability and random processes.