December 1, 2020

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Stochastic Modelling in Process Technology

Stochastic Modelling in Process Technology
Author : Herold G. Dehling,Timo Gottschalk,Alex C. Hoffmann
Publisher : Elsevier
Release Date : 2007-07-03
Category : Mathematics
Total pages :290
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There is an ever increasing need for modelling complex processes reliably. Computational modelling techniques, such as CFD and MD may be used as tools to study specific systems, but their emergence has not decreased the need for generic, analytical process models. Multiphase and multicomponent systems, and high-intensity processes displaying a highly complex behaviour are becoming omnipresent in the processing industry. This book discusses an elegant, but little-known technique for formulating process models in process technology: stochastic process modelling. The technique is based on computing the probability distribution for a single particle's position in the process vessel, and/or the particle's properties, as a function of time, rather than - as is traditionally done - basing the model on the formulation and solution of differential conservation equations. Using this technique can greatly simplify the formulation of a model, and even make modelling possible for processes so complex that the traditional method is impracticable. Stochastic modelling has sporadically been used in various branches of process technology under various names and guises. This book gives, as the first, an overview of this work, and shows how these techniques are similar in nature, and make use of the same basic mathematical tools and techniques. The book also demonstrates how stochastic modelling may be implemented by describing example cases, and shows how a stochastic model may be formulated for a case, which cannot be described by formulating and solving differential balance equations. Introduction to stochastic process modelling as an alternative modelling technique Shows how stochastic modelling may be succesful where the traditional technique fails Overview of stochastic modelling in process technology in the research literature Illustration of the principle by a wide range of practical examples In-depth and self-contained discussions Points the way to both mathematical and technological research in a new, rewarding field

Markov Processes for Stochastic Modeling

Markov Processes for Stochastic Modeling
Author : Oliver Ibe
Publisher : Newnes
Release Date : 2013-05-22
Category : Mathematics
Total pages :514
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Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects. Therefore, this is an applications-oriented book that also includes enough theory to provide a solid ground in the subject for the reader. Presents both the theory and applications of the different aspects of Markov processes Includes numerous solved examples as well as detailed diagrams that make it easier to understand the principle being presented Discusses different applications of hidden Markov models, such as DNA sequence analysis and speech analysis.

Stochastic Modelling for Systems Biology, Second Edition

Stochastic Modelling for Systems Biology, Second Edition
Author : Darren J. Wilkinson
Publisher : CRC Press
Release Date : 2011-11-09
Category : Mathematics
Total pages :363
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Since the first edition of Stochastic Modelling for Systems Biology, there have been many interesting developments in the use of "likelihood-free" methods of Bayesian inference for complex stochastic models. Re-written to reflect this modern perspective, this second edition covers everything necessary for a good appreciation of stochastic kinetic modelling of biological networks in the systems biology context. Keeping with the spirit of the first edition, all of the new theory is presented in a very informal and intuitive manner, keeping the text as accessible as possible to the widest possible readership. New in the Second Edition All examples have been updated to Systems Biology Markup Language Level 3 All code relating to simulation, analysis, and inference for stochastic kinetic models has been re-written and re-structured in a more modular way An ancillary website provides links, resources, errata, and up-to-date information on installation and use of the associated R package More background material on the theory of Markov processes and stochastic differential equations, providing more substance for mathematically inclined readers Discussion of some of the more advanced concepts relating to stochastic kinetic models, such as random time change representations, Kolmogorov equations, Fokker-Planck equations and the linear noise approximation Simple modelling of "extrinsic" and "intrinsic" noise An effective introduction to the area of stochastic modelling in computational systems biology, this new edition adds additional mathematical detail and computational methods that will provide a stronger foundation for the development of more advanced courses in stochastic biological modelling.

Stochastic Modelling for Systems Biology, Third Edition

Stochastic Modelling for Systems Biology, Third Edition
Author : Darren J. Wilkinson
Publisher : CRC Press
Release Date : 2018-12-07
Category : Mathematics
Total pages :384
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Since the first edition of Stochastic Modelling for Systems Biology, there have been many interesting developments in the use of "likelihood-free" methods of Bayesian inference for complex stochastic models. Having been thoroughly updated to reflect this, this third edition covers everything necessary for a good appreciation of stochastic kinetic modelling of biological networks in the systems biology context. New methods and applications are included in the book, and the use of R for practical illustration of the algorithms has been greatly extended. There is a brand new chapter on spatially extended systems, and the statistical inference chapter has also been extended with new methods, including approximate Bayesian computation (ABC). Stochastic Modelling for Systems Biology, Third Edition is now supplemented by an additional software library, written in Scala, described in a new appendix to the book. New in the Third Edition New chapter on spatially extended systems, covering the spatial Gillespie algorithm for reaction diffusion master equation models in 1- and 2-d, along with fast approximations based on the spatial chemical Langevin equation Significantly expanded chapter on inference for stochastic kinetic models from data, covering ABC, including ABC-SMC Updated R package, including code relating to all of the new material New R package for parsing SBML models into simulatable stochastic Petri net models New open-source software library, written in Scala, replicating most of the functionality of the R packages in a fast, compiled, strongly typed, functional language Keeping with the spirit of earlier editions, all of the new theory is presented in a very informal and intuitive manner, keeping the text as accessible as possible to the widest possible readership. An effective introduction to the area of stochastic modelling in computational systems biology, this new edition adds additional detail and computational methods that will provide a stronger foundation for the development of more advanced courses in stochastic biological modelling.

Stochastic Modelling of Electricity and Related Markets

Stochastic Modelling of Electricity and Related Markets
Author : Fred Espen Benth,Jurate Saltyte Benth,Steen Koekebakker
Publisher : World Scientific
Release Date : 2008
Category : Technology & Engineering
Total pages :337
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The markets for electricity, gas and temperature have distinctive features, which provide the focus for countless studies. For instance, electricity and gas prices may soar several magnitudes above their normal levels within a short time due to imbalances in supply and demand, yielding what is known as spikes in the spot prices. The markets are also largely influenced by seasons, since power demand for heating and cooling varies over the year. The incompleteness of the markets, due to nonstorability of electricity and temperature as well as limited storage capacity of gas, makes spot-forward hedging impossible. Moreover, futures contracts are typically settled over a time period rather than at a fixed date. All these aspects of the markets create new challenges when analyzing price dynamics of spot, futures and other derivatives. This book provides a concise and rigorous treatment on the stochastic modeling of energy markets. OrnsteinOCoUhlenbeck processes are described as the basic modeling tool for spot price dynamics, where innovations are driven by time-inhomogeneous jump processes. Temperature futures are studied based on a continuous higher-order autoregressive model for the temperature dynamics. The theory presented here pays special attention to the seasonality of volatility and the Samuelson effect. Empirical studies using data from electricity, temperature and gas markets are given to link theory to practice. Sample Chapter(s). A Survey of Electricity and Related Markets (331 KB). Contents: A Survey of Electricity and Related Markets; Stochastic Analysis for Independent Increment Processes; Stochastic Models for the Energy Spot Price Dynamics; Pricing of Forwards and Swaps Based on the Spot Price; Applications to the Gas Markets; Modeling Forwards and Swaps Using the HeathOCoJarrowOCoMorton Approach; Constructing Smooth Forward Curves in Electricity Markets; Modeling of the Electricity Futures Market; Pricing and Hedging of Energy Options; Analysis of Temperature Derivatives. Readership: Researchers in energy and commodity markets, and mathematical finance.

Deterministic Versus Stochastic Modelling in Biochemistry and Systems Biology

Deterministic Versus Stochastic Modelling in Biochemistry and Systems Biology
Author : Paulo Lecca,Ian Laurenzi,Ferenc Jordan
Publisher : Elsevier
Release Date : 2013-04-09
Category : Mathematics
Total pages :390
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Stochastic kinetic methods are currently considered to be the most realistic and elegant means of representing and simulating the dynamics of biochemical and biological networks. Deterministic versus stochastic modelling in biochemistry and systems biology introduces and critically reviews the deterministic and stochastic foundations of biochemical kinetics, covering applied stochastic process theory for application in the field of modelling and simulation of biological processes at the molecular scale. Following an overview of deterministic chemical kinetics and the stochastic approach to biochemical kinetics, the book goes onto discuss the specifics of stochastic simulation algorithms, modelling in systems biology and the structure of biochemical models. Later chapters cover reaction-diffusion systems, and provide an analysis of the Kinfer and BlenX software systems. The final chapter looks at simulation of ecodynamics and food web dynamics. Introduces mathematical concepts and formalisms of deterministic and stochastic modelling through clear and simple examples Presents recently developed discrete stochastic formalisms for modelling biological systems and processes Describes and applies stochastic simulation algorithms to implement a stochastic formulation of biochemical and biological kinetics

Stochastic Models In Engineering, Technology And Management - Proceedings Of The Australia-japan Workshop

Stochastic Models In Engineering, Technology And Management - Proceedings Of The Australia-japan Workshop
Author : Osaki Shunji,Murthy D N Pra
Publisher : World Scientific
Release Date : 1993-04-27
Category :
Total pages :628
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Chinese Remainder Theorem, CRT, is one of the jewels of mathematics. It is a perfect combination of beauty and utility or, in the words of Horace, omne tulit punctum qui miscuit utile dulci. Known already for ages, CRT continues to present itself in new contexts and open vistas for new types of applications. So far, its usefulness has been obvious within the realm of “three C's”. Computing was its original field of application, and continues to be important as regards various aspects of algorithmics and modular computations. Theory of codes and cryptography are two more recent fields of application.This book tells about CRT, its background and philosophy, history, generalizations and, most importantly, its applications. The book is self-contained. This means that no factual knowledge is assumed on the part of the reader. We even provide brief tutorials on relevant subjects, algebra and information theory. However, some mathematical maturity is surely a prerequisite, as our presentation is at an advanced undergraduate or beginning graduate level. We have tried to make the exposition innovative, many of the individual results being new. We will return to this matter, as well as to the interdependence of the various parts of the book, at the end of the Introduction.A special course about CRT can be based on the book. The individual chapters are largely independent and, consequently, the book can be used as supplementary material for courses in algorithmics, coding theory, cryptography or theory of computing. Of course, the book is also a reference for matters dealing with CRT.

Energy Efficiency in Process Technology

Energy Efficiency in Process Technology
Author : P.A. Pilavachi
Publisher : Springer Science & Business Media
Release Date : 2012-12-06
Category : Science
Total pages :1280
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Since 1975 the Commission has been stimulating R & D work aimed at energy saving. The conference objective was to provide an international forum for the presentation and discussion of recent R & D relevant to energy efficiency, taking into account environmental aspects, in the energy intensive process industries.

GPS Stochastic Modelling

GPS Stochastic Modelling
Author : Xiaoguang Luo
Publisher : Springer Science & Business Media
Release Date : 2013-07-06
Category : Technology & Engineering
Total pages :331
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Global Navigation Satellite Systems (GNSS), such as GPS, have become an efficient, reliable and standard tool for a wide range of applications. However, when processing GNSS data, the stochastic model characterising the precision of observations and the correlations between them is usually simplified and incomplete, leading to overly optimistic accuracy estimates. This work extends the stochastic model using signal-to-noise ratio (SNR) measurements and time series analysis of observation residuals. The proposed SNR-based observation weighting model significantly improves the results of GPS data analysis, while the temporal correlation of GPS observation noise can be efficiently described by means of autoregressive moving average (ARMA) processes. Furthermore, this work includes an up-to-date overview of the GNSS error effects and a comprehensive description of various mathematical methods.

Modeling Random Processes for Engineers and Managers

Modeling Random Processes for Engineers and Managers
Author : James J. Solberg
Publisher : John Wiley & Sons
Release Date : 2008-12-22
Category : Technology & Engineering
Total pages :320
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By reducing mathematical detail and focusing on real-world applications, this book provides engineers with an easy-to-understand overview of stochastic modeling. An entire chapter is included on how to set up the problem, and then another complete chapter presents examples of applications before doing any math. A previously unpublished computational method for solving equations related to Markov processes is added. The book shows how to add costs or revenues to the basic probability structures without much additional effort. In addition, numerous examples are included that show how the theory can be used. Engineers will also find explanations on how to formulate word problems into the models that the math worked on.

Stochastic Models of Financial Mathematics

Stochastic Models of Financial Mathematics
Author : Vigirdas Mackevicius
Publisher : Elsevier
Release Date : 2016-11-08
Category : Mathematics
Total pages :130
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This book presents a short introduction to continuous-time financial models. An overview of the basics of stochastic analysis precedes a focus on the Black-Scholes and interest rate models. Other topics covered include self-financing strategies, option pricing, exotic options and risk-neutral probabilities. Vasicek, Cox-Ingersoll-Ross, and Heath-Jarrow-Morton interest rate models are also explored. The author presents practitioners with a basic introduction, with more rigorous information provided for mathematicians. The reader is assumed to be familiar with the basics of probability theory. Some basic knowledge of stochastic integration and differential equations theory is preferable, although all preliminary information is given in the first part of the book. Some relatively simple theoretical exercises are also provided. About continuous-time stochastic models of financial mathematics Black-Sholes model and interest rate models Requiring a minimum knowledge of stochastic integration and stochastic differential equations

Stochastic Processes

Stochastic Processes
Author : Robert G. Gallager
Publisher : Cambridge University Press
Release Date : 2013-12-12
Category : Technology & Engineering
Total pages :568
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This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.

Advances in Stochastic Modelling and Data Analysis

Advances in Stochastic Modelling and Data Analysis
Author : Jacques Janssen,Christos H. Skiadas,Constantin Zopounidis
Publisher : Springer Science & Business Media
Release Date : 2013-04-17
Category : Mathematics
Total pages :428
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Advances in Stochastic Modelling and Data Analysis presents the most recent developments in the field, together with their applications, mainly in the areas of insurance, finance, forecasting and marketing. In addition, the possible interactions between data analysis, artificial intelligence, decision support systems and multicriteria analysis are examined by top researchers. Audience: A wide readership drawn from theoretical and applied mathematicians, such as operations researchers, management scientists, statisticians, computer scientists, bankers, marketing managers, forecasters, and scientific societies such as EURO and TIMS.

Stochastic Models in Reliability Engineering

Stochastic Models in Reliability Engineering
Author : Lirong Cui,Ilia Frenkel,Anatoly Lisnianski
Publisher : CRC Press
Release Date : 2020-09-01
Category : Mathematics
Total pages :464
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This book is a collective work by many leading scientists, analysts, mathematicians, and engineers who have been working at the front end of reliability science and engineering. The book covers conventional and contemporary topics in reliability science, all of which have seen extended research activities in recent years. The methods presented in this book are real-world examples that demonstrate improvements in essential reliability and availability for industrial equipment such as medical magnetic resonance imaging, power systems, traction drives for a search and rescue helicopter, and air conditioning systems. The book presents real case studies of redundant multi-state air conditioning systems for chemical laboratories and covers assessments of reliability and fault tolerance and availability calculations. Conventional and contemporary topics in reliability engineering are discussed, including degradation, networks, and dynamic reliability, resilience, and multi-state systems, all of which are relatively new topics to the field. The book is aimed at engineers and scientists, as well as postgraduate students involved in reliability design, analysis, and experiments and applied probability and statistics.

Stochastic Processes in Science, Engineering and Finance

Stochastic Processes in Science, Engineering and Finance
Author : Frank Beichelt
Publisher : CRC Press
Release Date : 2006-02-22
Category : Mathematics
Total pages :440
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This book presents a self-contained introduction to stochastic processes with emphasis on their applications in science, engineering, finance, computer science, and operations research. It provides theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates their application by analyzing numerous practical examples. The treatment assumes few prerequisites, requiring only the standard mathematical maturity acquired by undergraduate applied science students. It includes an introductory chapter that summarizes the basic probability theory needed as background. Numerous exercises reinforce the concepts and techniques discussed and allow readers to assess their grasp of the subject. Solutions to most of the exercises are provided in an appendix. While focused primarily on practical aspects, the presentation includes some important proofs along with more challenging examples and exercises for those more theoretically inclined. Mastering the contents of this book prepares readers to apply stochastic modeling in their own fields and enables them to work more creatively with software designed for dealing with the data analysis aspects of stochastic processes.