INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9781447153610
NATIONAL BIBLIOGRAPHY NUMBER
Country Code
IR
Number
EN-52549
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
COUNTRY OF PUBLICATION OR PRODUCTlON
Country of publication
IR
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Probability Theor
General Material Designation
[Book]
Other Title Information
:A Comprehensive Course
First Statement of Responsibility
/ electronic resource
EDITION STATEMENT
Edition Statement
2. ed. 2014.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
London
Name of Publisher, Distributor, etc.
: Springer London :Imprint: Springer,
Date of Publication, Distribution, etc.
, 2014.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
XII, 638 s. 46 illus., 20 illus. in color. , online resource..
SERIES
Series Title
(Universitext,0172-5939)
GENERAL NOTES
Text of Note
9781447153603.
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
CONTENTS NOTE
Text of Note
Summary: This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms. a To address these concepts, the title covers a wide variety of topics, many of which are not usually found in introductory textbooks, such as: a @2022 limit theorems for sums of random variables @2022 martingales @2022 percolation @2022 Markov chains and electrical networks @2022 construction of stochastic processes @2022 Poisson point process and infinite divisibility @2022 large deviation principles and statistical physics @2022 Brownian motion @2022 stochastic integral and stochastic differential equations. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology.
Text of Note
Basic Measure Theory -- Independence -- Generating Functions -- The Integral -- Moments and Laws of Large Numbers -- Convergence Theorems -- Lp-Spaces and the Radon@2013Nikodym Theorem -- Conditional Expectations -- Martingales -- Optional Sampling Theorems -- Martingale Convergence Theorems and Their Applications -- Backwards Martingales and Exchangeability -- Convergence of Measures -- Probability Measures on Product Spaces -- Characteristic Functions and the Central Limit Theorem -- Infinitely Divisible Distributions -- Markov Chains -- Convergence of Markov Chains -- Markov Chains and Electrical Networks -- Ergodic Theory -- Brownian Motion -- Law of the Iterated Logarithm -- Large Deviations -- The Poisson Point Process -- The It@02C6o Integral -- Stochastic Differential Equations.
SERIES
Title
Universitext,0172-5939
TOPICAL NAME USED AS SUBJECT
Mathematics
Differentiable dynamical systems
Functional analysis
Distribution (Probability theory)
Mathematics
Probability Theory and Stochastic Processes
Measure and Integration
Dynamical Systems and Ergodic Theory
Functional Analysis
Statistical Physics, Dynamical Systems and Complexity
LIBRARY OF CONGRESS CLASSIFICATION
Class number
E-BOOK
PERSONAL NAME - PRIMARY RESPONSIBILITY
Klenke, Achim.
PERSONAL NAME - SECONDARY RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Country
ایران
ELECTRONIC LOCATION AND ACCESS
Host name
9781447153603.pdf
Access number
عادی
Compression information
عادی
Date and Hour of Consultation and Access
9781447153603.pdf
Electronic Format Type
متن
old catalog
e
BL
1
a
Y
