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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Contents
I  1 
IV  4 
V  8 
VI  13 
VII  14 
VIII  16 
IX  21 
X  26 
LXXIII  296 
LXXIV  305 
LXXVI  308 
LXXVII  318 
LXXVIII  325 
LXXIX  329 
LXXX  332 
LXXXI  333 
XII  30 
XIII  33 
XIV  35 
XV  38 
XVI  41 
XVII  43 
XVIII  46 
XX  48 
XXI  50 
XXII  56 
XXIII  60 
XXIV  62 
XXV  67 
XXVI  70 
XXVII  71 
XXVIII  75 
XXIX  83 
XXX  89 
XXXII  91 
XXXIII  93 
XXXIV  95 
XXXV  98 
XXXVI  104 
XXXVII  107 
XXXVIII  113 
XXXIX  115 
XL  119 
XLI  122 
XLII  127 
XLIII  133 
XLIV  140 
XLV  148 
XLVII  156 
XLVIII  162 
XLIX  171 
L  175 
LI  178 
LII  181 
LIII  186 
LIV  189 
LV  193 
LVI  201 
LVII  206 
LVIII  213 
LX  220 
LXI  223 
LXII  227 
LXIII  237 
LXIV  240 
LXV  243 
LXVI  246 
LXVII  256 
LXVIII  266 
LXIX  268 
LXX  274 
LXXI  281 
LXXII  291 
LXXXII  338 
LXXXIII  343 
LXXXIV  350 
LXXXV  354 
LXXXVI  360 
LXXXVII  361 
LXXXVIII  365 
LXXXIX  367 
XC  370 
XCI  371 
XCII  373 
XCIII  375 
XCV  377 
XCVI  380 
XCVII  387 
XCVIII  393 
XCIX  405 
C  409 
CI  412 
CIII  417 
CIV  421 
CV  423 
CVI  431 
CVII  437 
CVIII  440 
CIX  442 
CX  445 
CXI  451 
CXII  455 
CXIII  462 
CXV  468 
CXVI  471 
CXVII  476 
CXVIII  481 
CXIX  487 
CXX  491 
CXXI  496 
CXXII  499 
CXXIII  503 
CXXIV  508 
CXXV  513 
CXXVII  514 
CXXVIII  516 
CXXIX  525 
CXXX  530 
CXXXI  534 
CXXXII  561 
CXXXIII  564 
CXXXIV  569 
CXXXV  571 
CXXXVI  573 
CXXXVII  576 
CXXXVIII  578 
CXXXIX  580 
CXL  583 
585  
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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