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Essentials of Stochastic Processes

IEssentials of Stochastic ProcessesRick Durrett304050607010 Sep10 Jun10 Mayat expiry0102050052054056058060062064066068 0700 Almost Final Version of the 2nd Edition, December, 2011 Copyright 2011, All rights the first undergraduate course in probability and the first graduatecourse that uses measure theory, there are a number of courses that teachStochastic Processesto students with many different interests and with varyingdegrees of mathematical sophistication. To allow readers (and instructors) tochoose their own level of detail, many of the proofs begin with a nonrigorousanswer to the question Why is this true? followed by aProofthat fills inthe missing details. As it is possible to drive a car without knowing about theworking of the internal combustion engine, it is also possible to apply the theoryof markov chains without knowing the details of the proofs. It is my personalphilosophy that probability theory was developed to solve problems, so most ofour effort will be spent on analyzing examples.

Chapter 1 Markov Chains 1.1 Definitions and Examples The importance of Markov chains comes from two facts: (i) there are a large number of physical, biological, economic, and social phenomena that can be modeled in this way, and (ii) there is a well-developed theory that allows us to do computations.

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