First Look at Rigorous Probability Theory

Edition: 2nd 2006

Authors: Jeffrey S. Rosenthal

30 day, 100% satisfaction guarantee

If an item you ordered from TextbookRush does not meet your expectations due to an error on our part, simply fill out a return request and then return it by mail within 30 days of ordering it for a full refund of item cost.

Description:

This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail.
New Starting from \$34.51
what's this?
Rush Rewards U
You have reached 400 XP and carrot coins. That is the daily max!
Study Briefs

Limited time offer: Get the first one free! (?)

All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.

Periodic Table Online content \$4.95 \$1.99
Calculus 1 Online content \$4.95 \$1.99
SQL Online content \$4.95 \$1.99
MS Excel® 2010 Online content \$4.95 \$1.99
Customers also bought

Book details

Edition: 2nd
Publisher: World Scientific Publishing Company, Incorporated
Binding: Paperback
Pages: 219
Size: 6.00" wide x 8.75" long x 0.75" tall
Weight: 0.946
Language: English

 Preface to the First Edition Preface to the Second Edition The need for measure theory Various kinds of random variables The uniform distribution and non-measurable sets Exercises Section summary Probability triples Basic definition Constructing probability triples The Extension Theorem Constructing the Uniform[0, 1] distribution Extensions of the Extension Theorem Coin tossing and other measures Exercises Section summary Further probabilistic foundations Random variables Independence Continuity of probabilities Limit events Tail fields Exercises Section summary Expected values Simple random variables General non-negative random variables Arbitrary random variables The integration connection Exercises Section summary Inequalities and convergence Various inequalities Convergence of random variables Laws of large numbers Eliminating the moment conditions Exercises Section summary Distributions of random variables Change of variable theorem Examples of distributions Exercises Section summary Stochastic processes and gambling games A first existence theorem Gambling and gambler's ruin Gambling policies Exercises Section summary Discrete Markov chains A Markov chain existence theorem Transience, recurrence, and irreducibility Stationary distributions and convergence Existence of stationary distributions Exercises Section summary More probability theorems Limit theorems Differentiation of expectation Moment generating functions and large deviations Fubini's Theorem and convolution Exercises Section summary Weak convergence Equivalences of weak convergence Connections to other convergence Exercises Section summary Characteristic functions The continuity theorem The Central Limit Theorem Generalisations of the Central Limit Theorem Method of moments Exercises Section summary Decomposition of probability laws Lebesgue and Hahn decompositions Decomposition with general measures Exercises Section summary Conditional probability and expectation Conditioning on a random variable Conditioning on a sub-[sigma]-algebra Conditional variance Exercises Section summary Martingales Stopping times Martingale convergence Maximal inequality Exercises Section summary General stochastic processes Kolmogorov Existence Theorem Markov chains on general state spaces Continuous-time Markov processes Brownian motion as a limit Existence of Brownian motion Diffusions and stochastic integrals Ito's Lemma The Black-Scholes equation Section summary Mathematical Background Sets and functions Countable sets Epsilons and Limits Infimums and supremums Equivalence relations Bibliography Background in real analysis Undergraduate-level probability Graduate-level probability Pure measure theory Stochastic processes Mathematical finance Index
Free shipping on orders over \$35*

*A minimum purchase of \$35 is required. Shipping is provided via FedEx SmartPost® and FedEx Express Saver®. Average delivery time is 1 – 5 business days, but is not guaranteed in that timeframe. Also allow 1 - 2 days for processing. Free shipping is eligible only in the continental United States and excludes Hawaii, Alaska and Puerto Rico. FedEx service marks used by permission."Marketplace" orders are not eligible for free or discounted shipping.