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Field name	Details
Dewey Class	519.2
Title	Probability Theory ([Ebook]) : A Comprehensive Course / by Achim Klenke.
Author	Klenke, Achim
Other name(s)	SpringerLink (Online service)
Publication	London : Springer , 2008.
Physical Details	xii, 616 pages : online resource.
Series	Universitext
ISBN	9781848000483
Summary Note	Probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us to understand magnetism, amorphous media, genetic diversity and the perils of random developments on the financial markets, and they guide us in constructing more efficient algorithms. This text is a comprehensive course in modern probability theory and its measure-theoretical foundations. Aimed primarily at graduate students and researchers, the book covers a wide variety of topics, many of which are not usually found in introductory textbooks, such as: limit theorems for sums of random variables; martingales; percolation; Markov chains and electrical networks; construction of stochastic processes; Poisson point processes and infinite divisibility; large deviation principles and statistical physics; Brownian motion; and 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 the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation.:
Contents note	Basic Measure Theory -- Independence -- Generating Functions -- The Integral -- Moments and Laws of Large Numbers -- Convergence Theorems -- Lp-Spaces and Radon-Nikodym 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 -- Characteristics Functions and 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 ItÃ´ Integral -- Stochastic Differential Equations -- References -- Notation Index -- Name Index -- Subject Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-84800-048-3
Links to Related Works	Subject References: Distribution (Probability theory) . Mathematical Statistics . Mathematics . Probabilities . Probability theory and stochastic processes . Statistical Physics, Dynamical Systems and Complexity . Statistical Theory and Methods . Authors: Klenke, Achim . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 519.2 . 519.2 (DDC 23) .

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Probability Theory: A Comprehensive Course

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