A First Look at Rigorous Probability Theory

Contents:The Need for Measure TheoryProbability TriplesFurther Probabilistic FoundationsExpected ValuesInequalities and ConvergenceDistributions of Random VariablesStochastic Processes and Gambling GamesDiscrete Markov ChainsMore Probability TheoremsWeak ConvergenceCharacteristic FunctionsDecomposition of Probability LawsConditional Probability and ExpectationMartingalesGeneral Stochastic Processes
Readership: Graduate students in mathematics, statistics, economics, management, finance, computer science and engineering.Probability Theory;Measure Theory;Random Variable;Expected Value;Law of Large Numbers;Central Limit Theorem;Markov Chain;Martingale;Stochastic Processes;Black-Scholes Equation0Key Features:Double the number of exercises compared to the 1st editionIncludes additional small topics and expands existing ones, and further details and explanations are inserted in steps of proofs for clarityLonger proofs are broken up into a number of lemmas for easy tracking of different steps and to allow for the possibility of skipping technical partsA few proofs are marked “optional” when an advanced mathematics background is requiredThe Extension Theorem now allows the original set function to be defined on a semialgebra rather on an algebra, thus simplifying its application and increasing the reader's understandingVarious interesting, though technical and inessential, results are presented as remarks or footnotes, to add information and context without interrupting the flow of the text