|
Showing 1 - 5 of
5 matches in All Departments
The material in this book is designed for a standard graduate
course on probability theory, including some important
applications. It was prepared from the sets of lecture notes for a
course that I have taught several times over the past 20 years. The
present version reflects the reactions of my audiences as well as
some of the textbooks that I used.
In response to unanswered difficulties in the generalized case of
conditional expectation and to treat the topic in a well-deservedly
thorough manner, M.M. Rao gave us the highly successful first
edition of Conditional Measures and Applications. Until this
groundbreaking work, conditional probability was relegated to
scattered journal articles and mere chapters in larger works on
probability. This second edition continues to offer a thorough
treatment of conditioning while adding substantial new information
on developments and applications that have emerged over the past
decade. Conditional Measures and Applications, Second Edition
clearly elucidates the subject, from fundamental principles to
abstract analysis. The author illustrates the computational
difficulties in evaluating conditional probabilities in nondiscrete
cases with numerous examples, demonstrates applications to Markov
processes, martingales, potential theory, and Reynolds operators as
well as sufficiency in statistics, and clarifies ideas in modern
noncommutative probability structures through conditioning in
general structures, including parts of operator algebras and "free"
random variables. He also discusses existence and construction
problems from the Bishop-Brouwer constructive analysis point of
view. With open problems in every chapter and links to other areas
of mathematics, this invaluable second edition offers complete
coverage of conditional probability and expectation and their
structural analysis, from simple to advanced abstract levels, for
both novices and seasoned mathematicians.
Significantly revised and expanded, this authoritative
reference/text comprehensively describes concepts in measure
theory, classical integration, and generalized Riemann integration
of both scalar and vector types-providing a complete and detailed
review of every aspect of measure and integration theory using
valuable examples, exercises, and applications. With more than 170
references for further investigation of the subject, this Second
Edition -provides more than 60 pages of new information, as well as
a new chapter on nonabsolute integrals -contains extended
discussions on the four basic results of Banach spaces -presents an
in-depth analysis of the classical integrations with many
applications, including integration of nonmeasurable functions,
Lebesgue spaces, and their properties -details the basic properties
and extensions of the Lebesgue-Caratheodory measure theory, as well
as the structure and convergence of real measurable functions
-covers the Stone isomorphism theorem, the lifting theorem, the
Daniell method of integration, and capacity theory Measure Theory
and Integration, Second Edition is a valuable reference for all
pure and applied mathematicians, statisticians, and mathematical
analysts, and an outstanding text for all graduate students in
these disciplines.
As in the case of the two previous volumes published in 1986 and
1997, the purpose of this monograph is to focus the interplay
between real (functional) analysis and stochastic analysis show
their mutual benefits and advance the subjects. The presentation of
each article, given as a chapter, is in a research-expository style
covering the respective topics in depth. In fact, most of the
details are included so that each work is essentially self
contained and thus will be of use both for advanced graduate
students and other researchers interested in the areas considered.
Moreover, numerous new problems for future research are suggested
in each chapter. The presented articles contain a substantial
number of new results as well as unified and simplified accounts of
previously known ones. A large part of the material cov ered is on
stochastic differential equations on various structures, together
with some applications. Although Brownian motion plays a key role,
(semi-) martingale theory is important for a considerable extent.
Moreover, noncommutative analysis and probabil ity have a prominent
role in some chapters, with new ideas and results. A more detailed
outline of each of the articles appears in the introduction and
outline to assist readers in selecting and starting their work. All
chapters have been reviewed."
|
You may like...
Morbius
Jared Leto, Matt Smith, …
DVD
R179
Discovery Miles 1 790
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
|