Meyn S P Tweedie R L Markov Chains and Stochastic Stability.pdf

Preface
Books are individual and idiosyncratic. In trying to understand what makes a good
book, there is a limited amount that one can learn from other books; but at least one
can read their prefaces, in hope of help.
Our own research shows that authors use prefaces for many different reasons.
Prefaces can be explanations of the role and the contents of the book, as in Chung
[49] or Revuz [223] or Nummelin [202]; this can bined with what is almost an
apology for bothering the reader, as in Billingsley [25] or C¸ inlar [40]; prefaces can
describe the mathematics, as in Orey [208], or the importance of the applications,
as in Tong [267] or Asmussen [10], or the way in which the book works as a text,
as in Brockwell and Davis [32] or Revuz [223]; they can be the only available outlet
for thanking those who made the task of writing possible, as in almost all of the
above (although we particularly like the familial gratitude of Resnick [222] and the
dedication of Simmons [240]); they bine all these roles, and many more.
This preface is no different. Let us begin with those we hope will use the book.
Who wants this stuff anyway?
This book is about Markov chains on general state spaces: sequences Φn evolving
randomly in time which remember their past trajectory only through its most recent
value. We develop their theoretical structure and we describe their application.
The theory of general state space chains has matured over the past twenty years
in ways which make it very much more accessible, very much plete, and (we
at least think) rather beautiful to learn and use. We have tried to convey all of this,
and to convey it at a level that is no more difficult than the corresponding countable
space theory.
The easiest reader for us to envisage is the long-suffering graduate student, who
is expected, in many disciplines, to take a course on countable space Markov chains.
Such a graduate student should be able to read almost all of the general space