Probability and Random ProcessesThe third edition of this successful text gives a rigorous introduction to probability theory and the discussion of the most important random processes in some depth. It includes various topics which are suitable for undergraduate courses, but are not routinely taught. It is suitable to the beginner, and provides a taste and encouragement for more advanced work. There are four main aims: 1) to provide a thorough but straightforward account of basic probability, giving the reader a natural feel for the subject unburdened by oppressive technicalities, 2) to discuss important random processes in depth with many examples. 3) to cover a range of important but less routine topics, 4) to impart to the beginner the flavour of more advanced work. The books begins with basic ideas common to many undergraduate courses in mathematics, statistics and the sciences; in concludes with topics usually found at graduate level. The ordering and numbering of material in this third edition has been mostly preserved from the second. Minor alterations and additions have been added for clearer exposition. Highlights include new sections on sampling and Markov chain Monte Carlo, geometric probability, coupling and Poisson approximation, large deviations, spatial Poisson processes, renewalreward, queueing networks, stochastic calculus, Itô's formula and option pricing in the BlackScholes model for financial markets. In addition there are many (nearly 400) new exercises and problems that are entertaining and instructive; their solutions can be found in the companion volume 'One Thousand Exercises in Probability', (OUP 2001). 
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Review: Probability and Random Processes
User Review  Jeff Rogers  GoodreadsThe content is good, but dense, particularly if it's your first introduction to probability. Should definitely get the companion book containing all the exercises and their solutions. Read full review
Review: Probability and Random Processes
User Review  Qubitng  GoodreadsFar too difficult as a standard course in undergraduate probability. Some of the exercises have an indulgent/noninstructive feel to them; for example, the very first exercise in section 4.14 is to ... Read full review
Contents
I  1 
IV  4 
V  8 
VI  13 
VII  14 
VIII  16 
IX  21 
X  26 
LXXIII  296 
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CX  445 
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CXXXIX  580 
CXL  583 
585  
Common terms and phrases
afield arrival assume branching process calculate called characteristic function comains cominuous conditional expectation constam convergence deduce define Definition denote density function distribution function distribution with parameter equation ergodic evem event Example Exercises for Section exists exponemial exponentially distributed finite function F given imegers imegrable imensity imerval independem random variables independent indicator function inequality integral interarrival irreducible large numbers Lemma Let Xn Markov chain Markov property martingale mass function momem nonnegative normal distribution notation obtain particle persistem poim Poisson distribution Poisson process probability generating function probability space Problem Proof queue random walk real numbers renewal process result sample paths satisfies sequence Show solution standard Wiener process stationary distribution stationary process stochastic strongly stationary submartingale subsets Suppose taking values Theorem theory tosses transition matrix tsee variance vector Wiener process zero means