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Author : Suman Das
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (16 download)
Download or read book Orthogonal Decompositions for Generalized Stochastic Processes with Independent Values written by Suman Das and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (111 download)
Download or read book Orthogonal Decompositions for Generalized Stochastic Processes with Independent Values written by and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert B. Ash
Publisher :
ISBN 13 :
Total Pages : 338 pages
Book Rating : 4.3/5 (91 download)
Download or read book Topics in Stochastic Processes written by Robert B. Ash and published by . This book was released on 1975 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Processes, Introduction, Covariance functions, Second order calculus, Karhunen-loeve expansion, Estimation problems, Notes; Spectral theory and prediction, Introduction, L Stochastic integrals, Decomposition of stationary processes, Examples of discrete parameter processes, Discrete parameter prediction: Special cases, Discrete parameter prediction: General solution, Examples of continuous parameter processes; Continuos parameter prediction special cases; yaglom's method, Some stochastic differential equations, Continuos parameter prediction: remarks on the general solution, Notes; Ergodic theory, Ergodicity and mixing, The pointwise ergodic theorem, Applications to real analysis, Applications to Markov chains, The Shannon-mcMillan theorem, Notes; Sample function analysis of continuous parameter stochastic processes, Separability, Measurability, One-Dimensional brownian motion, Law of the iterated logarithm, Markov processes, Processes with independent increments, Continuous parameter martingales, The strong Markov property, Notes; The ito integral and stochastic differential equations, Definitions of the ito integral, Existence and uniqueness theorems for stochastic differential equations, Stochastic differentials: A chain rule, Notes.
Author : Grigorios A. Pavliotis
Publisher : Springer
ISBN 13 : 1493913239
Total Pages : 345 pages
Book Rating : 4.4/5 (939 download)
Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
Author : Tucker S. McElroy
Publisher : CRC Press
ISBN 13 : 1439876525
Total Pages : 587 pages
Book Rating : 4.4/5 (398 download)
Download or read book Time Series written by Tucker S. McElroy and published by CRC Press. This book was released on 2019-12-09 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time Series: A First Course with Bootstrap Starter provides an introductory course on time series analysis that satisfies the triptych of (i) mathematical completeness, (ii) computational illustration and implementation, and (iii) conciseness and accessibility to upper-level undergraduate and M.S. students. Basic theoretical results are presented in a mathematically convincing way, and the methods of data analysis are developed through examples and exercises parsed in R. A student with a basic course in mathematical statistics will learn both how to analyze time series and how to interpret the results. The book provides the foundation of time series methods, including linear filters and a geometric approach to prediction. The important paradigm of ARMA models is studied in-depth, as well as frequency domain methods. Entropy and other information theoretic notions are introduced, with applications to time series modeling. The second half of the book focuses on statistical inference, the fitting of time series models, as well as computational facets of forecasting. Many time series of interest are nonlinear in which case classical inference methods can fail, but bootstrap methods may come to the rescue. Distinctive features of the book are the emphasis on geometric notions and the frequency domain, the discussion of entropy maximization, and a thorough treatment of recent computer-intensive methods for time series such as subsampling and the bootstrap. There are more than 600 exercises, half of which involve R coding and/or data analysis. Supplements include a website with 12 key data sets and all R code for the book's examples, as well as the solutions to exercises.
Author : Svante Janson
Publisher : American Mathematical Soc.
ISBN 13 : 082182595X
Total Pages : 90 pages
Book Rating : 4.8/5 (218 download)
Download or read book Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics written by Svante Janson and published by American Mathematical Soc.. This book was released on 1994 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define an orthogonal basis in the space of real-valued functions of a random graph, and prove a functional limit theorem for this basis. Limit theorems for other functions then follow by decomposition. The results include limit theorems for the two random graph models [italic]G[subscript italic]n, [subscript italic]p and [italic]G[subscript italic]n, [subscript italic]m as well as functional limit theorems for the evolution of a random graph and results on the maximum of a function during the evolution. Both normal and non-normal limits are obtained. As examples, applications are given to subgraph counts and to vertex degrees.
Author : Qing Huang
Publisher :
ISBN 13 :
Total Pages : 113 pages
Book Rating : 4.:/5 (853 download)
Download or read book Some Topics Concerning the Singular Value Decomposition and Generalized Singular Value Decomposition written by Qing Huang and published by . This book was released on 2012 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation involves three problems that are all related by the use of the singular value decomposition (SVD) or generalized singular value decomposition (GSVD). The specific problems are (i) derivation of a generalized singular value expansion (GSVE), (ii) analysis of the properties of the chi-squared method for regularization parameter selection in the case of nonnormal data and (iii) formulation of a partial canonical correlation concept for continuous time stochastic processes. The finite dimensional SVD has an infinite dimensional generalization to compact operators. However, the form of the finite dimensional GSVD developed in, e.g., Van Loan does not extend directly to infinite dimensions as a result of a key step in the proof that is specific to the matrix case. Thus, the first problem of interest is to find an infinite dimensional version of the GSVD. One such GSVE for compact operators on separable Hilbert spaces is developed. The second problem concerns regularization parameter estimation. The chi-squared method for nonnormal data is considered. A form of the optimized regularization criterion that pertains to measured data or signals with nonnormal noise is derived. Large sample theory for phi-mixing processes is used to derive a central limit theorem for the chi-squared criterion that holds under certain conditions. Departures from normality are seen to manifest in the need for a possibly different scale factor in normalization rather than what would be used under the assumption of normality. The consequences of our large sample work are illustrated by empirical experiments. For the third problem, a new approach is examined for studying the relationships between a collection of functional random variables. The idea is based on the work of Sunder that provides mappings to connect the elements of algebraic and orthogonal direct sums of subspaces in a Hilbert space. When combined with a key isometry associated with a particular Hilbert space indexed stochastic process, this leads to a useful formulation for situations that involve the study of several second order processes. In particular, using our approach with two processes provides an independent derivation of the functional canonical correlation analysis (CCA) results of Eubank and Hsing. For more than two processes, a rigorous derivation of the functional partial canonical correlation analysis (PCCA) concept that applies to both finite and infinite dimensional settings is obtained.
Author : Jim Pitman
Publisher : Springer Science & Business Media
ISBN 13 : 354030990X
Total Pages : 257 pages
Book Rating : 4.5/5 (43 download)
Download or read book Combinatorial Stochastic Processes written by Jim Pitman and published by Springer Science & Business Media. This book was released on 2006-05-11 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.
Author : Jason L. Speyer
Publisher : SIAM
ISBN 13 : 0898718597
Total Pages : 392 pages
Book Rating : 4.8/5 (987 download)
Download or read book Stochastic Processes, Estimation, and Control written by Jason L. Speyer and published by SIAM. This book was released on 2008-01-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty and risk are integral to engineering because real systems have inherent ambiguities that arise naturally or due to our inability to model complex physics. The authors discuss probability theory, stochastic processes, estimation, and stochastic control strategies and show how probability can be used to model uncertainty in control and estimation problems. The material is practical and rich in research opportunities.
Author : Wim Schoutens
Publisher : Springer
ISBN 13 : 038795015X
Total Pages : 184 pages
Book Rating : 4.3/5 (879 download)
Download or read book Stochastic Processes and Orthogonal Polynomials written by Wim Schoutens and published by Springer. This book was released on 2000-05-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been known for a long time that there is a close connection between stochastic processes and orthogonal polynomials. For example, N. Wiener [112] and K. Ito [56] knew that Hermite polynomials play an important role in the integration theory with respect to Brownian motion. In the 1950s D. G. Kendall [66], W. Ledermann and G. E. H. Reuter [67] [74], and S. Kar lin and J. L. McGregor [59] established another important connection. They expressed the transition probabilities of a birth and death process by means of a spectral representation, the so-called Karlin-McGregor representation, in terms of orthogonal polynomials. In the following years these relation ships were developed further. Many birth and death models were related to specific orthogonal polynomials. H. Ogura [87], in 1972, and D. D. En gel [45], in 1982, found an integral relation between the Poisson process and the Charlier polynomials. Some people clearly felt the potential im portance of orthogonal polynomials in probability theory. For example, P. Diaconis and S. Zabell [29] related Stein equations for some well-known distributions, including Pearson's class, with the corresponding orthogonal polynomials. The most important orthogonal polynomials are brought together in the so-called Askey scheme of orthogonal polynomials. This scheme classifies the hypergeometric orthogonal polynomials that satisfy some type of differ ential or difference equation and stresses the limit relations between them.
Author : John L. Lumey
Publisher : Elsevier
ISBN 13 : 0323162258
Total Pages : 209 pages
Book Rating : 4.3/5 (231 download)
Download or read book Stochastic Tools in Turbulence written by John L. Lumey and published by Elsevier. This book was released on 2012-12-02 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the characteristic function, and the Gaussian distribution from a more physical point of view. In considering fields, one must account for single-valued functions of one or more parameters, or collections of single-valued functions of one or more parameters such as time or space coordinates. The text also discusses multidimensional vector fields of finite energy, the characteristic eddies for a homogenous vector field, as well as, the distribution of solutions of an algebraic equation. Engineers, algebra students, and professors of statistics and advanced mathematics will find the book highly useful.
Author :
Publisher :
ISBN 13 :
Total Pages : 672 pages
Book Rating : 4.3/5 (91 download)
Download or read book Russian Mathematical Surveys written by and published by . This book was released on 2003 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bert E. Fristedt
Publisher :
ISBN 13 :
Total Pages : 76 pages
Book Rating : 4.:/5 (336 download)
Download or read book Generalized Variations, Continuity, and Hausdorff Measures of Sample Functions of Stochastic Processes with Independent Increments written by Bert E. Fristedt and published by . This book was released on 1963 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Riccardo Gatto
Publisher : World Scientific
ISBN 13 : 9811251851
Total Pages : 415 pages
Book Rating : 4.8/5 (112 download)
Download or read book Stationary Stochastic Models: An Introduction written by Riccardo Gatto and published by World Scientific. This book was released on 2022-06-23 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a unified mathematical introduction to stationary time series models and to continuous time stationary stochastic processes. The analysis of these stationary models is carried out in time domain and in frequency domain. It begins with a practical discussion on stationarity, by which practical methods for obtaining stationary data are described. The presented topics are illustrated by numerous examples. Readers will find the following covered in a comprehensive manner:At the end, some selected topics such as stationary random fields, simulation of Gaussian stationary processes, time series for planar directions, large deviations approximations and results of information theory are presented. A detailed appendix containing complementary materials will assist the reader with many technical aspects of the book.
Author : Malempati M. Rao
Publisher : Springer Science & Business Media
ISBN 13 : 1475765983
Total Pages : 629 pages
Book Rating : 4.4/5 (757 download)
Download or read book Stochastic Processes: General Theory written by Malempati M. Rao and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role: a unique feature of the book. Applications to higher order stochastic differential equations and their special features are presented in detail. Stochastic processes in a manifold and multiparameter stochastic analysis are also discussed. Each of the seven chapters includes complements, exercises and extensive references: many avenues of research are suggested. The book is a completely revised and enlarged version of the author's Stochastic Processes and Integration (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material. Audience: Suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.
Author : Fima C. Klebaner
Publisher : Imperial College Press
ISBN 13 : 1860945554
Total Pages : 431 pages
Book Rating : 4.8/5 (69 download)
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.
Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)
Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
