Random Probability Measures On Polish Spaces
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Random Probability Measures on Polish Spaces
Author | : Hans Crauel |
Publsiher | : CRC Press |
Total Pages | : 138 |
Release | : 2002-07-25 |
Genre | : Mathematics |
ISBN | : 0203219112 |
Download Random Probability Measures on Polish Spaces Book in PDF, Epub and Kindle
In this monograph the narrow topology on random probability measures on Polish spaces is investigated in a thorough and comprehensive way. As a special feature, no additional assumptions on the probability space in the background, such as completeness or a countable generated algebra, are made. One of the main results is a direct proof of the rando
Mathematics of Two Dimensional Turbulence
Author | : Sergei Kuksin,Armen Shirikyan |
Publsiher | : Cambridge University Press |
Total Pages | : 337 |
Release | : 2012-09-20 |
Genre | : Mathematics |
ISBN | : 9781139576956 |
Download Mathematics of Two Dimensional Turbulence Book in PDF, Epub and Kindle
This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier–Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) – proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.
A Modern Approach to Probability Theory
Author | : Bert E. Fristedt,Lawrence F. Gray |
Publsiher | : Springer Science & Business Media |
Total Pages | : 780 |
Release | : 1996-12-23 |
Genre | : Mathematics |
ISBN | : 0817638075 |
Download A Modern Approach to Probability Theory Book in PDF, Epub and Kindle
Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.
The Poisson Dirichlet Distribution and Related Topics
Author | : Shui Feng |
Publsiher | : Springer Science & Business Media |
Total Pages | : 228 |
Release | : 2010-05-27 |
Genre | : Mathematics |
ISBN | : 9783642111945 |
Download The Poisson Dirichlet Distribution and Related Topics Book in PDF, Epub and Kindle
Presenting a comprehensive study of the Poisson-Dirichlet distribution, this volume emphasizes recent progress in evolutionary dynamics and asymptotic behaviors. The self-contained text presents methods and techniques that appeal to researchers in a wide variety of subjects.
Stable Convergence and Stable Limit Theorems
Author | : Erich Häusler,Harald Luschgy |
Publsiher | : Springer |
Total Pages | : 228 |
Release | : 2015-06-09 |
Genre | : Mathematics |
ISBN | : 9783319183299 |
Download Stable Convergence and Stable Limit Theorems Book in PDF, Epub and Kindle
The 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.
Advances in Disordered Systems Random Processes and Some Applications
Author | : Pierluigi Contucci,Cristian Giardinà |
Publsiher | : Cambridge University Press |
Total Pages | : 383 |
Release | : 2016-12-15 |
Genre | : Science |
ISBN | : 9781107124103 |
Download Advances in Disordered Systems Random Processes and Some Applications Book in PDF, Epub and Kindle
This book offers a unified perspective on the study of complex systems with contributions written by leading scientists from various disciplines, including mathematics, physics, computer science, biology, economics and social science. It is written for researchers from a broad range of scientific fields with an interest in recent developments in complex systems.
Probabilistic Symmetries and Invariance Principles
Author | : Olav Kallenberg |
Publsiher | : Springer Science & Business Media |
Total Pages | : 520 |
Release | : 2005-12-15 |
Genre | : Mathematics |
ISBN | : 9780387288611 |
Download Probabilistic Symmetries and Invariance Principles Book in PDF, Epub and Kindle
"This is the first comprehensive treatment of the three basic symmetries of probability theory - contractability, exchangeability, and rotatability - defined as invariance in distribution under contractions, permutations, and rotations. Most chapters require only some basic, graduate level probability theory, and should be accessible to any serious researchers and graduate students in probability and statistics. Parts of the book may also be of interest to pure and applied mathematicians in other areas. The exposition is formally self-contained, with detailed references provided for any deeper facts from real analysis or probability used in the book."--Jacket.
Fundamentals of Nonparametric Bayesian Inference
Author | : Subhashis Ghosal,Aad van der Vaart |
Publsiher | : Cambridge University Press |
Total Pages | : 671 |
Release | : 2017-06-26 |
Genre | : Business & Economics |
ISBN | : 9780521878265 |
Download Fundamentals of Nonparametric Bayesian Inference Book in PDF, Epub and Kindle
Bayesian nonparametrics comes of age with this landmark text synthesizing theory, methodology and computation.