Download or read book Monotonicity Properties of Infinitely Divisible Distributions written by B. G. Hansen and published by . This book was released on 1990 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Monotonicity Properties of Infinitely Divisible Distributions written by Bjørn Gårn Hansen and published by . This book was released on 1988 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Monotonicity properties of infinitely divisible distributions written by Björn Garn Hansen and published by . This book was released on 1988 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Infinite Divisibility of Probability Distributions on the Real Line written by Fred W. Steutel and published by CRC Press. This book was released on 2003-10-03 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite Divisibility of Probability Distributions on the Real Line reassesses classical theory and presents new developments, while focusing on divisibility with respect to convolution or addition of independent random variables. This definitive, example-rich text supplies approximately 100 examples to correspond with all major chapter topics and reviews infinite divisibility in light of the central limit problem. It contrasts infinite divisibility with finite divisibility, discusses the preservation of infinite divisibility under mixing for many classes of distributions, and investigates self-decomposability and stability on the nonnegative reals, nonnegative integers, and the reals.

Download or read book Monotonicity Proporties of Infinitely Divisible Distributions written by B. G. Hansen and published by . This book was released on 1988 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topics in Infinitely Divisible Distributions and L vy Processes Revised Edition written by Alfonso Rocha-Arteaga and published by Springer Nature. This book was released on 2019-11-02 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with topics in the area of Lévy processes and infinitely divisible distributions such as Ornstein-Uhlenbeck type processes, selfsimilar additive processes and multivariate subordination. These topics are developed around a decreasing chain of classes of distributions Lm, m = 0,1,...,∞, from the class L0 of selfdecomposable distributions to the class L∞ generated by stable distributions through convolution and convergence. The book is divided into five chapters. Chapter 1 studies basic properties of Lm classes needed for the subsequent chapters. Chapter 2 introduces Ornstein-Uhlenbeck type processes generated by a Lévy process through stochastic integrals based on Lévy processes. Necessary and sufficient conditions are given for a generating Lévy process so that the OU type process has a limit distribution of Lm class. Chapter 3 establishes the correspondence between selfsimilar additive processes and selfdecomposable distributions and makes a close inspection of the Lamperti transformation, which transforms selfsimilar additive processes and stationary type OU processes to each other. Chapter 4 studies multivariate subordination of a cone-parameter Lévy process by a cone-valued Lévy process. Finally, Chapter 5 studies strictly stable and Lm properties inherited by the subordinated process in multivariate subordination. In this revised edition, new material is included on advances in these topics. It is rewritten as self-contained as possible. Theorems, lemmas, propositions, examples and remarks were reorganized; some were deleted and others were newly added. The historical notes at the end of each chapter were enlarged. This book is addressed to graduate students and researchers in probability and mathematical statistics who are interested in learning more on Lévy processes and infinitely divisible distributions.

Download or read book Probability in Banach Spaces 8 Proceedings of the Eighth International Conference written by R.M. Dudley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly.

Download or read book On Stein s Method for Infinitely Divisible Laws with Finite First Moment written by Benjamin Arras and published by Springer. This book was released on 2019-04-24 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on quantitative approximation results for weak limit theorems when the target limiting law is infinitely divisible with finite first moment. Two methods are presented and developed to obtain such quantitative results. At the root of these methods stands a Stein characterizing identity discussed in the third chapter and obtained thanks to a covariance representation of infinitely divisible distributions. The first method is based on characteristic functions and Stein type identities when the involved sequence of random variables is itself infinitely divisible with finite first moment. In particular, based on this technique, quantitative versions of compound Poisson approximation of infinitely divisible distributions are presented. The second method is a general Stein's method approach for univariate selfdecomposable laws with finite first moment. Chapter 6 is concerned with applications and provides general upper bounds to quantify the rate of convergence in classical weak limit theorems for sums of independent random variables. This book is aimed at graduate students and researchers working in probability theory and mathematical statistics.

Download or read book Classifying Infinitely Divisible Distributions by Functional Equations written by Klaas van Harn and published by . This book was released on 1978 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Generalized Gamma Convolutions and Related Classes of Distributions and Densities written by Lennart Bondesson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Gamma convolutions were introduced by Olof Thorin in 1977 and were used by him to show that, in particular, the Lognormal distribution is infinitely divisible. After that a large number of papers rapidly appeared with new results in a somewhat random order. Many of the papers appeared in the Scandinavian Actuarial Journal. This work is an attempt to present the main results on this class of probability distributions and related classes in a rather logical order. The goal has been to be on a level that is not too advanced. However, since the field is rather technical, most readers will find difficult passages in the text. Those who do not want to visit a mysterious land situated between the land of probability theory and statistics and the land of classical analysis should not look at this work. When some years ago I submitted a survey to a journal it was suggested by the editor, K. Krickeberg, that it should be expanded to a book. However, at that time I was rather reluctant to do so since there remained so many problems to be solved or to be solved in a smoother way than before. Moreover, there was at that time some lack of probabilistic interpretations and applications. Many of the problems are now solved but still it is felt that more applications than those presented in the work could be found.

Download or read book Stochastic Orders and Applications written by Karl Mosler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: A bibliography on stochastic orderings. Was there a real need for it? In a time of reference databases as the MathSci or the Science Citation Index or the Social Science Citation Index the answer seems to be negative. The reason we think that this bibliog raphy might be of some use stems from the frustration that we, as workers in the field, have often experienced by finding similar results being discovered and proved over and over in different journals of different disciplines with different levels of mathematical so phistication and accuracy and most of the times without cross references. Of course it would be very unfair to blame an economist, say, for not knowing a result in mathematical physics, or vice versa, especially when the problems and the languages are so far apart that it is often difficult to recognize the analogies even after further scrutiny. We hope that collecting the references on this topic, regardless of the area of application, will be of some help, at least to pinpoint the problem. We use the term stochastic ordering in a broad sense to denote any ordering relation on a space of probability measures. Questions that can be related to the idea of stochastic orderings are as old as probability itself. Think for instance of the problem of comparing two gambles in order to decide which one is more favorable.

Download or read book Unimodality Convexity and Applications written by and published by Elsevier. This book was released on 1988-08-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the basic notions and tools of unimodality as they relate to probability and statistics are presented. In addition, many applications are covered; these include the use of unimodality to obtain monotonicity properties of power functions of multivariate tests, minimum volume confidence regions, and recurrence of symmetric random walks. The diversity of the applications will convince the reader that unimodality and convexity form an important tool in the hands of a researcher in probability and statistics.

Download or read book Unimodality of Probability Measures written by Emile M.J. Bertin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this monograph is Khinchin-type representation theorems. An abstract framework for unimodality, an example of applied functional analysis, is developed for the introduction of different types of unimodality and the study of their behaviour. Also, several useful consequences or ramifications tied to these notions are provided. Being neither an encyclopaedia, nor a historical overview, this book aims to serve as an understanding of the basic features of unimodality. Chapter 1 lays a foundation for the mathematical reasoning in the chapters following. Chapter 2 deals with the concept of Khinchin space, which leads to the introduction of beta-unimodality in Chapter 3. A discussion on several existing multivariate notions of unimodality concludes this chapter. Chapter 4 concerns Khinchin's classical unimodality, and Chapter 5 is devoted to discrete unimodality. Chapters 6 and 7 treat the concept of strong unimodality on R and to Ibragimov-type results characterising the probability measures which preserve unimodality by convolution, and the concept of slantedness, respectively. Most chapters end with comments, referring to historical aspects or supplying complementary information and open questions. A practical bibliography, as well as symbol, name and subject indices ensure efficient use of this volume. Audience: Both researchers and applied mathematicians in the field of unimodality will value this monograph, and it may be used in graduate courses or seminars on this subject too.

Download or read book White Noise Analysis Mathematics And Applications written by Takeyuki Hida and published by World Scientific. This book was released on 1990-06-30 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings contains articles on white noise analysis and related subjects. Applications in various branches of science are also discussed. White noise analysis stems from considering the time derivative of Brownian motion (“white noise”) as the basic ingredient of an infinite dimensional calculus. It provides a powerful mathematical tool for research fields such as stochastic analysis, potential theory in infinite dimensions and quantum field theory.

Download or read book An Introduction to Sparse Stochastic Processes written by Michael Unser and published by Cambridge University Press. This book was released on 2014-08-21 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a novel approach to sparsity, this comprehensive book presents the theory of stochastic processes that are ruled by linear stochastic differential equations, and that admit a parsimonious representation in a matched wavelet-like basis. Two key themes are the statistical property of infinite divisibility, which leads to two distinct types of behaviour - Gaussian and sparse - and the structural link between linear stochastic processes and spline functions, which is exploited to simplify the mathematical analysis. The core of the book is devoted to investigating sparse processes, including a complete description of their transform-domain statistics. The final part develops practical signal-processing algorithms that are based on these models, with special emphasis on biomedical image reconstruction. This is an ideal reference for graduate students and researchers with an interest in signal/image processing, compressed sensing, approximation theory, machine learning, or statistics.

Download or read book Approximation and Computation A Festschrift in Honor of Walter Gautschi written by R.V.M. Zahar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: R. V. M. Zahar* The sixty-fifth birthday of Walter Gautschi provided an opportune moment for an international symposium in his honor, to recognize his many contributions to mathematics and computer sciences. Conceived by John Rice and sponsored by Purdue University, the conference took place in West Lafayette from December 2 to 5, 1993, and was organized around the four main themes representing Professor Gautschi's principal research interests: Approximation, Orthogonal Polynomials, Quadrature and Special Functions. Thirty-eight speakers - colleagues, co-authors, research collaborators or doctoral students of Professor Gautschi - were invited to present articles at the conference, their lectures providing an approximately equal representation of the four disciplines. Five invited speakers, Germund Dahlquist, Philip Davis, Luigi Gatteschi, Werner Rheinboldt and Stephan Ruscheweyh, were unable to present their talks because of illness or other commitments, although Professors Dahlquist, Gatteschi and Ruscheweyh subsequently contributed arti cles to these proceedings. Thus, the final program contained thirty-three technical lectures, ten of which were plenary sessions. Approximately eighty scientists attended the conference, and for some ses sions - in particular, Walter's presentation of his entertaining and informative Reflections and Recollections - that number was complemented by many visitors and friends, as well as the family of the honoree. A surprise visit by Paul Erdos provided one of the highlights of the conference week. The ambiance at the sym posium was extremely collegial, due no doubt to the common academic interests and the personal friendships shared by the participants.

Download or read book L vy Processes and Infinitely Divisible Distributions written by Sato Ken-Iti and published by Cambridge University Press. This book was released on 1999 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: