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Author: Amarjit Budhiraja Publisher: Springer ISBN: 1493995790 Category : Mathematics Languages : en Pages : 574
Book Description
This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.
Author: Amarjit Budhiraja Publisher: Springer ISBN: 1493995790 Category : Mathematics Languages : en Pages : 574
Book Description
This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.
Author: Jerome Morio Publisher: Woodhead Publishing ISBN: 0081001118 Category : Technology & Engineering Languages : en Pages : 217
Book Description
Rare event probability (10-4 and less) estimation has become a large area of research in the reliability engineering and system safety domains. A significant number of methods have been proposed to reduce the computation burden for the estimation of rare events from advanced sampling approaches to extreme value theory. However, it is often difficult in practice to determine which algorithm is the most adapted to a given problem.Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach provides a broad up-to-date view of the current available techniques to estimate rare event probabilities described with a unified notation, a mathematical pseudocode to ease their potential implementation and finally a large spectrum of simulation results on academic and realistic use cases. Provides a broad overview of the practical approach of rare event methods. Includes algorithms that are applied to aerospace benchmark test cases Offers insight into practical tuning issues
Author: Baron Peters Publisher: Elsevier ISBN: 0444594701 Category : Technology & Engineering Languages : en Pages : 636
Book Description
Reaction Rate Theory and Rare Events bridges the historical gap between these subjects because the increasingly multidisciplinary nature of scientific research often requires an understanding of both reaction rate theory and the theory of other rare events. The book discusses collision theory, transition state theory, RRKM theory, catalysis, diffusion limited kinetics, mean first passage times, Kramers theory, Grote-Hynes theory, transition path theory, non-adiabatic reactions, electron transfer, and topics from reaction network analysis. It is an essential reference for students, professors and scientists who use reaction rate theory or the theory of rare events. In addition, the book discusses transition state search algorithms, tunneling corrections, transmission coefficients, microkinetic models, kinetic Monte Carlo, transition path sampling, and importance sampling methods. The unified treatment in this book explains why chemical reactions and other rare events, while having many common theoretical foundations, often require very different computational modeling strategies. Offers an integrated approach to all simulation theories and reaction network analysis, a unique approach not found elsewhere Gives algorithms in pseudocode for using molecular simulation and computational chemistry methods in studies of rare events Uses graphics and explicit examples to explain concepts Includes problem sets developed and tested in a course range from pen-and-paper theoretical problems, to computational exercises
Author: Gerardo Rubino Publisher: John Wiley & Sons ISBN: 9780470745410 Category : Mathematics Languages : en Pages : 278
Book Description
In a probabilistic model, a rare event is an event with a very small probability of occurrence. The forecasting of rare events is a formidable task but is important in many areas. For instance a catastrophic failure in a transport system or in a nuclear power plant, the failure of an information processing system in a bank, or in the communication network of a group of banks, leading to financial losses. Being able to evaluate the probability of rare events is therefore a critical issue. Monte Carlo Methods, the simulation of corresponding models, are used to analyze rare events. This book sets out to present the mathematical tools available for the efficient simulation of rare events. Importance sampling and splitting are presented along with an exposition of how to apply these tools to a variety of fields ranging from performance and dependability evaluation of complex systems, typically in computer science or in telecommunications, to chemical reaction analysis in biology or particle transport in physics. Graduate students, researchers and practitioners who wish to learn and apply rare event simulation techniques will find this book beneficial.
Author: Michael Falk Publisher: Birkhäuser ISBN: 3034877919 Category : Mathematics Languages : en Pages : 381
Book Description
Since the publication of the first edition of this seminar book, the theory and applications of extremes and rare events have seen increasing interest. Laws of Small Numbers gives a mathematically oriented development of the theory of rare events underlying various applications. The new edition incorporates numerous new results on about 130 additional pages. Part II, added in the second edition, discusses recent developments in multivariate extreme value theory.
Author: James Bucklew Publisher: Springer Science & Business Media ISBN: 1475740786 Category : Mathematics Languages : en Pages : 262
Book Description
This book presents a unified theory of rare event simulation and the variance reduction technique known as importance sampling from the point of view of the probabilistic theory of large deviations. It allows us to view a vast assortment of simulation problems from a unified single perspective.
Author: David J. Hand Publisher: Scientific American / Farrar, Straus and Giroux ISBN: 0374711399 Category : Mathematics Languages : en Pages : 288
Book Description
In The Improbability Principle, the renowned statistician David J. Hand argues that extraordinarily rare events are anything but. In fact, they're commonplace. Not only that, we should all expect to experience a miracle roughly once every month. But Hand is no believer in superstitions, prophecies, or the paranormal. His definition of "miracle" is thoroughly rational. No mystical or supernatural explanation is necessary to understand why someone is lucky enough to win the lottery twice, or is destined to be hit by lightning three times and still survive. All we need, Hand argues, is a firm grounding in a powerful set of laws: the laws of inevitability, of truly large numbers, of selection, of the probability lever, and of near enough. Together, these constitute Hand's groundbreaking Improbability Principle. And together, they explain why we should not be so surprised to bump into a friend in a foreign country, or to come across the same unfamiliar word four times in one day. Hand wrestles with seemingly less explicable questions as well: what the Bible and Shakespeare have in common, why financial crashes are par for the course, and why lightning does strike the same place (and the same person) twice. Along the way, he teaches us how to use the Improbability Principle in our own lives—including how to cash in at a casino and how to recognize when a medicine is truly effective. An irresistible adventure into the laws behind "chance" moments and a trusty guide for understanding the world and universe we live in, The Improbability Principle will transform how you think about serendipity and luck, whether it's in the world of business and finance or you're merely sitting in your backyard, tossing a ball into the air and wondering where it will land.
Author: Eva Jurczyk Publisher: Sourcebooks, Inc. ISBN: 1728238609 Category : Fiction Languages : en Pages : 336
Book Description
International Bestseller "With its countless revelations about the dusty realms of rare books, a likable librarian sleuth who has just the right balance of compassion and wit, and a library setting that is teeming with secrets, The Department of Rare Books and Special Collections is a rare treat for readers. I loved this book!"—Matthew Sullivan, author of Midnight at the Bright Ideas Bookstore Anxious People meets the delights of bookish fiction in a stunning debut following a librarian whose quiet life is turned upside down when a priceless manuscript goes missing. Soon she has to ask: what holds more secrets in the library—the ancient books shelved in the stacks, or the people who preserve them? Liesl Weiss long ago learned to be content working behind the scenes in the distinguished rare books department of a large university, managing details and working behind the scenes to make the head of the department look good. But when her boss has a stroke and she's left to run things, she discovers that the library's most prized manuscript is missing. Liesl tries to sound the alarm and inform the police about the missing priceless book, but is told repeatedly to keep quiet, to keep the doors open and the donors happy. But then a librarian unexpectedly stops showing up to work. Liesl must investigate both disappearances, unspooling her colleagues' pasts like the threads of a rare book binding as it becomes clear that someone in the department must be responsible for the theft. What Liesl discovers about the dusty manuscripts she has worked among for so long—and about the people who care for and revere them—shakes the very foundation on which she has built her life. The Department of Rare Books and Special Collections is a sparkling book-club read about a woman struggling to step out from behind the shadows of powerful and unreliable men, and reveals the dark edge of obsession running through the most devoted bookworms. February 2022 INDIE NEXT Selection January 2022 LIBRARY READS Selection January 2022 Loan Star Selection Pop Sugar 35 Must-Read Thrillers and Mystery Books
Author: Laura Thalassa Publisher: ISBN: 9781942662303 Category : Death Languages : en Pages : 502
Book Description
As the last horseman carries out his mission to wipe out humanity, he meets the one woman who is immune to his abilities in this long-awaited enemies-to-lovers romance.
Author: Amarjit Budhiraja
Author: Amarjit Budhiraja
Author: Jerome Morio
Author: Baron Peters
Author: Gerardo Rubino
Author: Michael Falk
Author: James Bucklew
Author: V. J. Pezoldt
Author: David J. Hand
Author: Eva Jurczyk
Author: Laura Thalassa