Download or read book Covariance Functions Variation and Stochastic Integration written by Graham Donald Allen and published by . This book was released on 1971 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Stochastic Calculus with Applications written by Fima C. Klebaner and published by Imperial College Press. This book was released on 2005 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Download or read book Introduction to Stochastic Integration written by Hui-Hsiung Kuo and published by Springer Science & Business Media. This book was released on 2006-02-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Also called Ito calculus, the theory of stochastic integration has applications in virtually every scientific area involving random functions. This introductory textbook provides a concise introduction to the Ito calculus. From the reviews: "Introduction to Stochastic Integration is exactly what the title says. I would maybe just add a ‘friendly’ introduction because of the clear presentation and flow of the contents." --THE MATHEMATICAL SCIENCES DIGITAL LIBRARY
Download or read book Gaussian Processes for Machine Learning written by Carl Edward Rasmussen and published by MIT Press. This book was released on 2005-11-23 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.
Download or read book Real and Stochastic AnalysisRecent Advances written by M.M. Rao and published by CRC Press. This book was released on 1997-03-06 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real and Stochastic Analysis: Recent Advances presents a carefully edited collection of research articles written by research mathematicians and highlighting advances in RSA. A balanced blend of both theory and applications, this book covers six aspects of stochastic analysis in depth and detail. The first chapters cover the state of the art in tracers analysis, stochastic modeling as it applies to AIDS epidemiology, and the current state of higher order SDEs. Subsequent chapters present a simple approach to Gaussian dichotomy, an overview of harmonizable processes, and stochastic Fubini and Green theorems. Common to all the chapters, the employment of functional analytic methods creates a unified approach. Each chapter includes detailed proofs. Throughout the book, a substantial amount of new material is presented, much of it for the first time. This forward-looking work presents current accounts of important areas of research, evaluates recent advances, and identifies research frontiers and new challenges.
Download or read book Stochastic Calculus via Regularizations written by Francesco Russo and published by Springer Nature. This book was released on 2022-11-15 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book constitutes an introduction to stochastic calculus, stochastic differential equations and related topics such as Malliavin calculus. On the other hand it focuses on the techniques of stochastic integration and calculus via regularization initiated by the authors. The definitions relies on a smoothing procedure of the integrator process, they generalize the usual Itô and Stratonovich integrals for Brownian motion but the integrator could also not be a semimartingale and the integrand is allowed to be anticipating. The resulting calculus requires a simple formalism: nevertheless it entails pathwise techniques even though it takes into account randomness. It allows connecting different types of pathwise and non pathwise integrals such as Young, fractional, Skorohod integrals, enlargement of filtration and rough paths. The covariation, but also high order variations, play a fundamental role in the calculus via regularization, which can also be applied for irregular integrators. A large class of Gaussian processes, various generalizations of semimartingales such that Dirichlet and weak Dirichlet processes are revisited. Stochastic calculus via regularization has been successfully used in applications, for instance in robust finance and on modeling vortex filaments in turbulence. The book is addressed to PhD students and researchers in stochastic analysis and applications to various fields.
Download or read book Stochastic Dynamics and Control written by Jian-Qiao Sun and published by Elsevier. This book was released on 2006-08-10 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress processes are also presented. Classical feedback control, active damping, covariance control, optimal control, sliding control of stochastic systems, feedback control of stochastic time-delayed systems, and probability density tracking control are studied. Many control results are new in the literature and included in this book for the first time. The book serves as a reference to the engineers who design and maintain structures subject to harsh random excitations including earthquakes, sea waves, wind gusts, and aerodynamic forces, and would like to reduce the damages of structural systems due to random excitations.· Comprehensive review of probability theory, and stochastic processes· Random vibrations· Structural reliability and fatigue, Non-Gaussian fatigue· Monte Carlo methods· Stochastic calculus and engineering applications· Stochastic feedback controls and optimal controls· Stochastic sliding mode controls· Feedback control of stochastic time-delayed systems· Probability density tracking control
Download or read book Stochastic Convergence written by Eugene Lukacs and published by Academic Press. This book was released on 2014-07-03 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Convergence, Second Edition covers the theoretical aspects of random power series dealing with convergence problems. This edition contains eight chapters and starts with an introduction to the basic concepts of stochastic convergence. The succeeding chapters deal with infinite sequences of random variables and their convergences, as well as the consideration of certain sets of random variables as a space. These topics are followed by discussions of the infinite series of random variables, specifically the lemmas of Borel-Cantelli and the zero-one laws. Other chapters evaluate the power series whose coefficients are random variables, the stochastic integrals and derivatives, and the characteristics of the normal distribution of infinite sums of random variables. The last chapter discusses the characterization of the Wiener process and of stable processes. This book will prove useful to mathematicians and advance mathematics students.
Download or read book Problems And Solutions In Stochastic Calculus With Applications written by Patrik Albin and published by World Scientific. This book was released on 2024-08-27 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems and Solutions in Stochastic Calculus with Applications exposes readers to simple ideas and proofs in stochastic calculus and its applications. It is intended as a companion to the successful original title Introduction to Stochastic Calculus with Applications (Third Edition) by Fima Klebaner. The current book is authored by three active researchers in the fields of probability, stochastic processes, and their applications in financial mathematics, mathematical biology, and more. The book features problems rooted in their ongoing research. Mathematical finance and biology feature pre-eminently, but the ideas and techniques can equally apply to fields such as engineering and economics.The problems set forth are accessible to students new to the subject, with most of the problems and their solutions centring on a single idea or technique at a time to enhance the ease of learning. While the majority of problems are relatively straightforward, more complex questions are also set in order to challenge the reader as their understanding grows. The book is suitable for either self-study or for instructors, and there are numerous opportunities to generate fresh problems by modifying those presented, facilitating a deeper grasp of the material.
Download or read book Stochastic Systems written by Mircea Grigoriu and published by Springer Science & Business Media. This book was released on 2012-05-15 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty is an inherent feature of both properties of physical systems and the inputs to these systems that needs to be quantified for cost effective and reliable designs. The states of these systems satisfy equations with random entries, referred to as stochastic equations, so that they are random functions of time and/or space. The solution of stochastic equations poses notable technical difficulties that are frequently circumvented by heuristic assumptions at the expense of accuracy and rigor. The main objective of Stochastic Systems is to promoting the development of accurate and efficient methods for solving stochastic equations and to foster interactions between engineers, scientists, and mathematicians. To achieve these objectives Stochastic Systems presents: A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis Probabilistic models for random variables and functions needed to formulate stochastic equations describing realistic problems in engineering and applied sciences Practical methods for quantifying the uncertain parameters in the definition of stochastic equations, solving approximately these equations, and assessing the accuracy of approximate solutions Stochastic Systems provides key information for researchers, graduate students, and engineers who are interested in the formulation and solution of stochastic problems encountered in a broad range of disciplines. Numerous examples are used to clarify and illustrate theoretical concepts and methods for solving stochastic equations. The extensive bibliography and index at the end of the book constitute an ideal resource for both theoreticians and practitioners.
Download or read book Finite Element Methods for Structures with Large Stochastic Variations written by Isaac Elishakoff and published by Oxford University Press, USA. This book was released on 2003 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method (FEM) can be successfully applied to various field problems in solid mechanics, fluid mechanics and electrical engineering. This text discusses finite element methods for structures with large stochastic variations.
Download or read book Stochastic Processes Theory and Methods written by D N Shanbhag and published by Gulf Professional Publishing. This book was released on 2001 with total page 990 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the series contains chapters on areas such as pareto processes, branching processes, inference in stochastic processes, Poisson approximation, Levy processes, and iterated random maps and some classes of Markov processes. Other chapters cover random walk and fluctuation theory, a semigroup representation and asymptomatic behavior of certain statistics of the Fisher-Wright-Moran coalescent, continuous-time ARMA processes, record sequence and their applications, stochastic networks with product form equilibrium, and stochastic processes in insurance and finance. Other subjects include renewal theory, stochastic processes in reliability, supports of stochastic processes of multiplicity one, Markov chains, diffusion processes, and Ito's stochastic calculus and its applications. c. Book News Inc.
Download or read book Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability written by Jerzy Neyman and published by Univ of California Press. This book was released on 1961 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Big Data in Omics and Imaging written by Momiao Xiong and published by CRC Press. This book was released on 2017-12-01 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Big Data in Omics and Imaging: Association Analysis addresses the recent development of association analysis and machine learning for both population and family genomic data in sequencing era. It is unique in that it presents both hypothesis testing and a data mining approach to holistically dissecting the genetic structure of complex traits and to designing efficient strategies for precision medicine. The general frameworks for association analysis and machine learning, developed in the text, can be applied to genomic, epigenomic and imaging data. FEATURES Bridges the gap between the traditional statistical methods and computational tools for small genetic and epigenetic data analysis and the modern advanced statistical methods for big data Provides tools for high dimensional data reduction Discusses searching algorithms for model and variable selection including randomization algorithms, Proximal methods and matrix subset selection Provides real-world examples and case studies Will have an accompanying website with R code The book is designed for graduate students and researchers in genomics, bioinformatics, and data science. It represents the paradigm shift of genetic studies of complex diseases– from shallow to deep genomic analysis, from low-dimensional to high dimensional, multivariate to functional data analysis with next-generation sequencing (NGS) data, and from homogeneous populations to heterogeneous population and pedigree data analysis. Topics covered are: advanced matrix theory, convex optimization algorithms, generalized low rank models, functional data analysis techniques, deep learning principle and machine learning methods for modern association, interaction, pathway and network analysis of rare and common variants, biomarker identification, disease risk and drug response prediction.
Download or read book Continuous Martingales and Brownian Motion written by Daniel Revuz and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion....This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises." –BULLETIN OF THE L.M.S.
Download or read book Nonlinear Dynamics and Stochastic Mechanics written by Wolfgang Kliemann and published by CRC Press. This book was released on 2018-05-04 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering systems have played a crucial role in stimulating many of the modern developments in nonlinear and stochastic dynamics. After 20 years of rapid progress in these areas, this book provides an overview of the current state of nonlinear modeling and analysis for mechanical and structural systems. This volume is a coherent compendium written by leading experts from the United States, Canada, Western and Eastern Europe, and Australia. The 22 articles describe the background, recent developments, applications, and future directions in bifurcation theory, chaos, perturbation methods, stochastic stability, stochastic flows, random vibrations, reliability, disordered systems, earthquake engineering, and numerics. The book gives readers a sophisticated toolbox that will allow them to tackle modeling problems in mechanical systems that use stochastic and nonlinear dynamics ideas. An extensive bibliography and index ensure this volume will remain a reference standard for years to come.
