9780198572220

Probability and Random Processes

by ;
  • ISBN13:

    9780198572220

  • ISBN10:

    0198572220

  • Edition: 3rd
  • Format: Paperback
  • Copyright: 8/2/2001
  • Publisher: Oxford University Press

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Purchase Benefits

  • Free Shipping On Orders Over $59!
    Your order must be $59 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • Get Rewarded for Ordering Your Textbooks! Enroll Now
  • We Buy This Book Back!
    In-Store Credit: $15.75
    Check/Direct Deposit: $15.00
List Price: $90.66 Save up to $36.26
  • Rent Book $54.40
    Add to Cart Free Shipping

    TERM
    PRICE
    DUE

Supplemental Materials

What is included with this book?

  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
  • The Rental copy of this book is not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Summary

This book gives an introduction to probability and its many practical application by providing a thorough, entertaining account of basic probability and important random processes, covering a range of important topics. Emphasis is on modelling rather than abstraction and there are new sections on sampling and Markov chain Monte Carlo, renewal-reward, queueing networks, stochastic calculus, and option pricing in the Black-Scholes model for financial markets. In addition, there are almost 400 exercises and problems relevant to the material. Solutions can be found in One Thousand Exercises in Probability.

Table of Contents

Events and their probabilities
Introduction
1(1)
Events as sets
1(3)
Probability
4(4)
Conditional probability
8(5)
Independence
13(1)
Completeness and product spaces
14(2)
Worked examples
16(5)
Problems
21(5)
Random variables and their distributions
Random variables
26(4)
The law of averages
30(3)
Discrete and continuous variables
33(2)
Worked examples
35(3)
Random vectors
38(3)
Monte Carlo simulation
41(2)
Problems
43(3)
Discrete random variables
Probability mass functions
46(2)
Independence
48(2)
Expectation
50(6)
Indicators and matching
56(4)
Examples of discrete variables
60(2)
Dependence
62(5)
Conditional distributions and conditional expectation
67(3)
Sums of random variables
70(1)
Simple random walk
71(4)
Random walk: counting sample paths
75(8)
Problems
83(6)
Continuous random variables
Probability density functions
89(2)
Independence
91(2)
Expectation
93(2)
Examples of continuous variables
95(3)
Dependence
98(6)
Conditional distributions and conditional expectation
104(3)
Functions of random variables
107(6)
Sums of random variables
113(2)
Multivariate normal distribution
115(4)
Distributions arising from the normal distribution
119(3)
Sampling from a distribution
122(5)
Coupling and Poisson approximation
127(6)
Geometrical probability
133(7)
Problems
140(8)
Generating functions and their applications
Generating functions
148(8)
Some applications
156(6)
Random walk
162(9)
Branching processes
171(4)
Age-dependent branching processes
175(3)
Expectation revisited
178(3)
Characteristic functions
181(5)
Examples of characteristic functions
186(3)
Inversion and continuity theorems
189(4)
Two limit theorems
193(8)
Large deviations
201(5)
Problems
206(7)
Markov chains
Markov processes
213(7)
Classification of states
220(3)
Classification of chains
223(4)
Stationary distributions and the limit theorem
227(10)
Reversibility
237(3)
Chains with finitely many states
240(3)
Branching processes revisited
243(3)
Birth processes and the Poisson process
246(10)
Continuous-time Markov chains
256(10)
Uniform semigroups
266(2)
Birth--death processes and imbedding
268(6)
Special processes
274(7)
Spatial Poisson processes
281(10)
Markov chain Monte Carlo
291(5)
Problems
296(9)
Convergence of random variables
Introduction
305(3)
Modes of convergence
308(10)
Some ancillary results
318(7)
Laws of large numbers
325(4)
The strong law
329(3)
The law of the iterated logarithm
332(1)
Martingales
333(5)
Martingale convergence theorem
338(5)
Prediction and conditional expectation
343(7)
Uniform integrability
350(4)
Problems
354(6)
Random processes
Introduction
360(1)
Stationary processes
361(4)
Renewal processes
365(2)
Queues
367(3)
The Wiener Process
370(1)
Existence of processes
371(2)
Problems
373(2)
Stationary processes
Introduction
375(2)
Linear prediction
377(3)
Autocovariances and spectra
380(7)
Stochastic integration and the spectral representation
387(6)
The ergodic theorem
393(12)
Gaussian processes
405(4)
Problems
409(3)
Renewals
The renewal equation
412(5)
Limit theorems
417(4)
Excess life
421(2)
Applications
423(8)
Renewal--reward processes
431(6)
Problems
437(3)
Queues
Single-server queues
440(2)
M/M/1
442(3)
M/G/1
445(6)
G/M/1
451(4)
G/G/1
455(7)
Heavy traffic
462(1)
Networks of queues
462(6)
Problems
468(3)
Martingales
Introduction
471(5)
Martingale differences and Hoeffding's inequality
476(5)
Crossings and convergence
481(6)
Stopping times
487(4)
Optional stopping
491(5)
The Maximal inequality
496(3)
Backward martingales and continuous-time martingales
499(4)
Some examples
503(5)
Problems
508(5)
Diffusion processes
Introduction
513(1)
Brownian motion
514(2)
Diffusion processes
516(9)
First passage times
525(5)
Barriers
530(4)
Excursions and the Brownian bridge
534(3)
Stochastic calculus
537(2)
The Ito integral
539(5)
Ito's formula
544(3)
Option pricing
547(7)
Passage probabilities and potentials
554(7)
Problems
561(3)
Appendix I. Foundations and notation 564(5)
Appendix II. Further reading 569(2)
Appendix III. History and varieties of probability 571(2)
Appendix IV. John Arbuthnot's Preface to Of the laws of chance (1692) 573(3)
Appendix V. Table of distributions 576(2)
Appendix VI. Chronology 578(2)
Bibliography 580(3)
Notation 583(2)
Index 585

Rewards Program

Write a Review