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 Topics in Infinitely Divisible Distributions and L vy Processes written by Alfonso Rocha-Arteaga and published by . This book was released on 2003 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
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 Infinitely Divisible Distributions and Stochastic Processes with Independent Increments written by Howard G. Tucker and published by . This book was released on 1970 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research project final report in the area of infinitely divisible distributions and stochastic processes with independent increments discusses various results of the principal investigator in stable distributions, distribution functions in class L, Martingale theory, etc. (Author).
Download or read book Exotic options infinitely divisible distributions and L vy processes theoretical and applied perspectives written by Guillaume Coqueret and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Infinite Divisibility and Unimodality of Certain Transformed Distributions written by Theodore Artikis and published by . This book was released on 1978 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The question concerning which distributions are unimodal, is answered by the Khintchine theorem of integral representation for characteristic functions of unimodal distributions. Similarly the question concerning the infinite divisibility of distributions is answered by the Levy representation theorem for infinitely divisible characteristic functions. However these theorems do not provide an answer to the question as to whether a given distribution function is both unimodal and infinitely divisible. One of the purposes of this thesis is to establish the unimodality and infinite divisibility of certain transformations of distribution functions. Special attention is given to mixtures of distributions. Chapter 1 is introductory. Chapter 2 is devoted to superposition of two distributions. In Chapter 3 we study the unimodality and infinite divisibility of transformations of distribution functions connected with the renewal distribution. Chapter 4 establishes the unimodality of an infinitely divisible transformation of characteristic functions. Chapter 5 deals with the concepts of complete monotonicity, log-convexity, and log-concavity. Chapter 6 is devoted to characterisations of infinitelydivisible distributions under unimodality. The discussion of the thesis and topics for further research are given in Chapter 7.
Download or read book Preservation of Infinite Divisibility Under Mixing and Related Topics written by F. W. Steutel and published by . This book was released on 1970 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book L vy Processes and Infinitely Divisible Distributions written by 健一·佐藤 and published by . This book was released on 1999-11-11 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book is intended to provide the reader with comprehensive basic knowledge of Lévy processes, and at the same time serve as an introduction to stochastic processes in general. No specialist knowledge is assumed and proofs are given in detail. Systematic study is made of stable and semi-stable processes, and the author gives special emphasis to the correspondence between Lévy processes and infinitely divisible distributions. All serious students of random phenomena will find that this book has much to offer. Now in paperback, this corrected edition contains a brand new supplement discussing relevant developments in the area since the book's initial publication.
Download or read book A Class of Infinitely Divisible Distributions Connected to Branching Processes and Random Walks written by Lennart Bondesson and published by . This book was released on 2002 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A New Decomposition of Infinitely Divisible Distributions written by Damodar N. Shanbhag and published by . This book was released on 1974 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Perspectives in Mathematical Sciences written by Yisong Yang and published by World Scientific. This book was released on 2010 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Periodic boundary problems for analytic function including automorphic functions / Haitao Cai and Jian-Ke Lu -- 2. Subharmonic bifurcations and chaos for a model of micro-cantilever in MEMS / Yushu Chen, Liangqiang Zhou and Fangqi Chen -- 3. Canonical sample spaces for random dynamical systems / Jinqiao Duan, Xingye Kan and Bjorn Schmalfuss -- 4. Epidemic propagation dynamics on complex networks / Xinchu Fu ... [et al.] -- 5. Inverse problems for equations of parabolic type / Zhibin Han, Yongzhong Huang and Ming Jian -- 6. The existence and asymptotic properties of nontrivial solutions of nonlinear (2 - q)-Laplacian type problems with linking geometric structure / Gongbao Li and Zhaofen Shen -- 7. Chaotic dynamics for the two-component Bose-Einstein condensate system / Jibin Li -- 8. Recent developments and perspectives in nonlinear dynamics / Zengrong Liu -- 9. Mathematical aspects of the cold plasma model / Thomas H. Otway -- 10. Gravitating Yang-Mills fields in all dimensions / Eugen Radu and D. H. Tchrakian -- 11. Hamiltonian constraint and Mandelstam identities over extended knot families [symbol] and [symbol] in extended loop gravity / Dan Shao, Liang Shao and Changgui Shao -- 12. Lattice Boltzmann simulation of nonlinear Schrödinger equation with variable coefficients / Baochang Shi -- 13. Exponential stability of nonlocal time-delayed burgers equation / Yanbin Tang -- 14. Bifurcation analysis of the Swift-Hohenberg equation with quintic nonlinearity and Neumann boundary condition / Qingkun Xiao and Hongjun Gao -- 15. A new GL method for mathematical and physical problems / Ganquan Xie and Jianhua Li -- 16. Harmonically representing topological classes / Yisong Yang.
Download or read book Numerical Methods for Infinitely Divisible Distributions written by and published by . This book was released on 2010 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Supports of Infinitely Divisible Distributions written by Herman Rubin and published by . This book was released on 1963 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been a considerable amount of recent interest in the problem of characterizing absolutely continuous infinitely divisible distributions by their Levy-Khintechine representation, and in the singular case, characterizing the dimension of the support. It is easy to give examples of infinitely divisible distributions of 0-dimensional support whose convolution is absolutely continuous. This work shows that the dimension of the marginals of a process of independ ent stationary increments can do anything consistent with dimension increasing on convolution and the marginals possibly becoming absolutely continuous. (Author).
Download or read book Quasi infinitely Divisible Distributions and Quasi L vy Measures written by Lei Pan and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Quasi infinitely Divisible Distributions written by Merve Kutlu and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fluctuations of L vy Processes with Applications written by Andreas E. Kyprianou and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.
