Strong Limit Theorems in Non-Commutative Probability
Author: R. Jajte
Publisher: Springer
Published: 2007-01-05
Total Pages: 159
ISBN-13: 3540391398
DOWNLOAD EBOOKRead and Download eBook Full
Author: R. Jajte
Publisher: Springer
Published: 2007-01-05
Total Pages: 159
ISBN-13: 3540391398
DOWNLOAD EBOOKAuthor: Ryszard Jajte
Publisher:
Published: 1985
Total Pages: 152
ISBN-13: 9780387139159
DOWNLOAD EBOOKAuthor: Ryszard Jajte
Publisher: Springer
Published: 2006-12-08
Total Pages: 122
ISBN-13: 3540475125
DOWNLOAD EBOOKThe noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.
Author: Alexander Bulinski
Publisher: World Scientific
Published: 2007-09-05
Total Pages: 447
ISBN-13: 9814474576
DOWNLOAD EBOOKThis volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications.There are 434 items in the bibliography.The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.).
Author: Erich Häusler
Publisher: Springer
Published: 2015-06-09
Total Pages: 231
ISBN-13: 331918329X
DOWNLOAD EBOOKThe authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level with a solid knowledge of measure theoretic probability.
Author: Luigi Accardi
Publisher: World Scientific
Published: 1994-12-16
Total Pages: 427
ISBN-13: 9814501301
DOWNLOAD EBOOKQuantum Probability and Related Topics is a series of volumes whose goal is to provide a picture of the state of the art in this rapidly growing field where classical probability, quantum physics and functional analysis merge together in an original synthesis which, for 20 years, has been enriching these three areas with new ideas, techniques and results.
Author: Lin Zhengyan
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 204
ISBN-13: 9401730970
DOWNLOAD EBOOKThis volume presents an up-to-date review of the most significant developments in strong Approximation and strong convergence in probability theory. The book consists of three chapters. The first deals with Wiener and Gaussian processes. Chapter 2 is devoted to the increments of partial sums of independent random variables. Chapter 3 concentrates on the strong laws of processes generated by infinite-dimensional Ornstein-Uhlenbeck processes. For researchers whose work involves probability theory and statistics.
Author: Andrei N. Frolov
Publisher: World Scientific Publishing Company
Published: 2020
Total Pages: 0
ISBN-13: 9789811212826
DOWNLOAD EBOOKStrong laws and large deviations -- Large deviations for sums of independent random variables -- Strong limit theorems for sums of independent random variables -- Strong limit theorems for processes with independent increments -- Strong limit theorems for renewal processes -- Increments of sums of independent random variables over head runs and monotone blocks.
Author: I. Cuculescu
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 367
ISBN-13: 9401583749
DOWNLOAD EBOOKThe intention of this book is to explain to a mathematician having no previous knowledge in this domain, what "noncommutative probability" is. So the first decision was not to concentrate on a special topic. For different people, the starting points of such a domain may be different. In what concerns this question, different variants are not discussed. One such variant comes from Quantum Physics. The motivations in this book are mainly mathematical; more precisely, they correspond to the desire of developing a probability theory in a new set-up and obtaining results analogous to the classical ones for the newly defined mathematical objects. Also different mathematical foundations of this domain were proposed. This book concentrates on one variant, which may be described as "von Neumann algebras". This is true also for the last chapter, if one looks at its ultimate aim. In the references there are some papers corresponding to other variants; we mention Gudder, S.P. &al (1978). Segal, I.E. (1965) also discusses "basic ideas".
Author: Tao Mei
Publisher: American Mathematical Soc.
Published: 2007
Total Pages: 78
ISBN-13: 0821839802
DOWNLOAD EBOOKThe author gives a systematic study of the Hardy spaces of functions with values in the noncommutative $Lp$-spaces associated with a semifinite von Neumann algebra $\mathcal{M .$ This is motivated by matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of noncommutative martingale inequalities. in this paper noncommutative Hardy spaces are defined by noncommutative Lusin integral function, and it isproved that they are equivalent to those defined by noncommutative Littlewood-Paley G-functions. The main results of this paper include: (i) The analogue in the author's setting of the classical Fefferman duality theorem between $\mathcal{H 1$ and $\mathrm{BMO $. (ii) The atomic decomposition of theauthor's noncommutative $\mathcal{H 1.$ (iii) The equivalence between the norms of the noncommutative Hardy spaces and of the noncommutative $Lp$-spaces $(1