Probability Theory: An Introductory CourseSpringer Science & Business Media, 2013 M03 9 - 140 páginas Sinai's book leads the student through the standard material for ProbabilityTheory, with stops along the way for interesting topics such as statistical mechanics, not usually included in a book for beginners. The first part of the book covers discrete random variables, using the same approach, basedon Kolmogorov's axioms for probability, used later for the general case. The text is divided into sixteen lectures, each covering a major topic. The introductory notions and classical results are included, of course: random variables, the central limit theorem, the law of large numbers, conditional probability, random walks, etc. Sinai's style is accessible and clear, with interesting examples to accompany new ideas. Besides statistical mechanics, other interesting, less common topics found in the book are: percolation, the concept of stability in the central limit theorem and the study of probability of large deviations. Little more than a standard undergraduate course in analysis is assumed of the reader. Notions from measure theory and Lebesgue integration are introduced in the second half of the text. The book is suitable for second or third year students in mathematics, physics or other natural sciences. It could also be usedby more advanced readers who want to learn the mathematics of probability theory and some of its applications in statistical physics. |
Otras ediciones - Ver todas
Términos y frases comunes
a₁ a₂ arbitrary assume b₁ Borel subsets C₁ C₂ called Central Limit Theorem characteristic function Chebyshev's inequality conditional probability consider converges Corollary countable d₁ d₂ defined Definition denote density distribution function dP(x E₁ elementary outcomes equal exists F₁ F₂ finite follows function F Furthermore graph independent identical trials independent random variables interval jointly independent k₁ K₂ Large Numbers Law of Large Lebesgue integral Lecture Lemma m₁ m₂ Markov chain mathematical expectation matrix multivariate normal distribution n₁ n₂ non-negative number of values o-algebra F obtain P₁ P₂ particles partition percolation polynomial probability distribution probability measure probability space probability theory problem Proof prove random walk sequence of independent simple random variables statement stochastic matrices summation variance vector w₁ W₂ Σ Σ