Theory of Probability and Random Processes

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Springer Science & Business Media, 10.08.2007 - 358 Seiten

The core of this book is a one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students. The book provides a comprehensive, self-contained exposition of classical probability theory and the theory of random processes, and dwells on a number of modern topics not addressed in most textbooks. There is detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory. It also includes the theory of stationary random processes, martingales, generalized random processes, and Brownian motion. One section is devoted to the theory of Gibbs random fields. The material is essential to many undergraduate and graduate courses. The book can also serve as a reference for scientists using modern probability theory in their research.

 

Ausgewählte Seiten

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Theory of Probability and Random Processes
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Theory of Probability and Random Processes
Leonid Koralov,Yakov G. Sinai
Keine Leseprobe verfügbar - 2008

Häufige Begriffe und Wortgruppen

A₁ assume Borel sets Brownian motion called characteristic function consider constant continuous function converge weakly countable covariance function cylindrical sets defined denoted density differential equation distributed random variables distribution function Dynkin system Ergodic Theorem exists filtration Ft finite finite-dimensional distributions formula function f identically distributed random implies independent identically distributed independent random variables indicator function Inequality interval Kolmogorov Large Numbers Law of Large Lebesgue measure Lemma Let us show Let Xt limn linear Markov chain Markov family martingale matrix measurable function measurable space o-algebra parameter probability distribution probability measure probability space process Xt Proof Prove random vector random walk right-continuous right-hand side satisfies sequence of independent solution stationary process subsets surely t₁ uniformly unique values variance wide-sense stationary Xt(w Εξ ξη

Beliebte Passagen

Seite 157 - I hope you now agree that the situation for the law of large numbers and the central limit theorem for...‎
Wird in 20 Büchern von 1931 bis 2007 erwähnt
Seite 58 - ... are then also independent. On this hypothesis, the formula for the mean value reduces according to (9.3.1) to (15.3.4) R' R" The extension to an arbitrary finite number of factors is immediate, so that we have the following theorem : The mean value of a product of independent random variables is equal to the product of the mean values of the factors, provided that the latter mean values exist. We finally consider some simple particular cases of the preceding general relations. — If...‎
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Seite 51 - X if for any e > 0 there is a 5 > 0 such that p(x,x^) < 5 implies P[/(X),/(X O )] < e.‎
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Seite 55 - T is continuous at x if for any e > 0 there is a 5 > 0 such that if \\y - x\\ < 5, then \\Ty - Tx\\ < e.‎
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Seite 259 - Let (/„)„';'. , be a sequence of independent, identically distributed random variables on a probability space...‎
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Seite 67 - P- is called the transition probability from the state "i" to the state "j‎
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Seite 122 - I <2dp(x\+\j 2dp(x) 99 99 which implies the statement of the lemma. D We now return to the proof of the theorem.‎
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Seite 137 - Let £i,£2, ... be a sequence of independent identically distributed random variables with zero expectation and finite variance. We define the random variables Then Cri+i — -=(Cn + Cn), where 2" £. SiClearly, (Jn and C^ are independent identically distributed random variables.‎
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Seite 219 - If we assume that the measure P is absolutely continuous (with respect to the Lebesgue measure...‎
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Autoren-Profil (2007)

YAKOV SINAI has been a professor at Princeton University since 1993. He was educated at Moscow State University, and was a professor there till 1993.
Since 1971 he has also held the position of senior researcher at the Landau Institute of Theoretical Physics. He is known for fundamental work on dynamical systems, probability theory, mathematical physics, and statistical mechanics. He has been awarded, among other honors, the Boltzmann Medal (in 1986) and Wolf Prize in Mathematics (in 1997). He is a member of Russian and American Academies of Sciences.

LEONID KORALOV is an assistant professor at the University of Maryland. From 2000 till 2006 he was an assistant professor at Princeton University, prior to which he worked at the Institute for Advanced Study in Princeton. He did his undergraduate work at Moscow State University, and got his PhD from SUNY at Stony Brook in 1998. He works on problems in the areas of homogenization, diffusion processes, and partial differential equations.

Bibliografische Informationen

TitelTheory of Probability and Random Processes
Mathematics and Statistics
Mathematics and Statistics (R0)
AutorenLeonid Koralov, Yakov G. Sinai
Ausgabe2, illustriert
VerlagSpringer Science & Business Media, 2007
ISBN3540688293, 9783540688297
Länge358 Seiten
  
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