Probability: An Introduction (2e) - Grimmet and Welsh

Probability: An Introduction, (2e)

by Geoffrey Grimmett and Dominic Welsh.

#Pages : 288
#Publisher : Oxford University Press, (2e) 2014
#ISBN-13 : 9780198709978
#Format : PDF

Probability is an area of mathematics of tremendous contemporary
importance across all aspects of human endeavour. This book is a
compact account of the basic features of probability and random
processes at the level of first and second year mathematics
undergraduates and Masters' students in cognate fields. It is suitable
for a first course in probability, plus a follow-up course in random
processes including Markov chains.

A special feature is the authors' attention to rigorous mathematics:
not everything is rigorous, but the need for rigour is explained at
difficult junctures. The text is enriched by simple exercises,
together with problems (with very brief hints) many of which are taken
from final examinations at Cambridge and Oxford.

The first eight chapters form a course in basic probability, being an
account of events, random variables, and distributions - discrete and
continuous random variables are treated separately - together with
simple versions of the law of large numbers and the central limit
theorem. There is an account of moment generating functions and
their applications. The following three chapters are about branching
processes, random walks, and continuous-time random processes such as
the Poisson process. The final chapter is a fairly extensive account
of Markov chains in discrete time.



This second edition develops the success of the first edition through
an updated presentation, the extensive new chapter on Markov chains,
and a number of new sections to ensure comprehensive coverage of the
syllabi at major universities.


Contents
========

PART I: Basic Probability
1. Events and Probabilities
2. Discrete Random Variables
3. Multivariate Discrete Distributions and Independence
4. Probability Generating Functions
5. Distribution Functions and Density Functions

PART II: Further Probability
6. Multivariate Distributions and Independence
7. Moments and Moment Generating Functions
8. The Two Main Limit Theorems

PART III: Random Processes
9. Branching Processes
10. Random Walks
11. Random Processes in Continuous Time


Authors
=======

Geoffrey Grimmett is Professor of Mathematical Statistics at the
University of Cambridge and Master of Downing College, Cambridge. His
reserach interests lie in disordered physical systems, including
percolation and related processes. He has written numerous research
articles in probability theory and statistical mechanics, as well as
three research books and two successful textbooks on probability and
random processes at the undergraduate and postgraduate levels.

Dominic Welsh held the John von Neumann Professorship at Bonn in
1990-91, and was appointed Professor of Mathematics at Oxford in 1993.
His research interests include combinatorics and complexity theory,
and he has written more than a hundred papers in these areas. He
retired from Oxford University in 2005, and has since then held
visiting positions in New Zealand and Barcelona.

-_-