Manyprobability books are written by mathematicians and have the
built-in bias that the reader is assumed to be a mathematician
coming to the material for its beauty. This textbook is geared
towards beginning graduate students from a variety of disciplines
whose primary focus is not necessarily mathematics for its own
sake. Instead, "A Probability Path" is designed for those requiring
a deep understanding of advanced probability for their research in
statistics, applied probability, biology, operations research,
mathematical finance and engineering.
A one-semester course is laid out in an efficient and readable
manner covering the core material. The first three chapters provide
a functioning knowledge of measure theory. Chapter 4 discusses
independence, with expectation and integration covered in Chapter
5, followed by topics on different modes of convergence, laws of
large numbers with applications to statistics (quantile and
distribution function estimation) and applied probability. Two
subsequent chapters offer a careful treatment of convergence in
distribution and the central limit theorem. The final chapter
treats conditional expectation and martingales, closing with a
discussion of two fundamental theorems of mathematical finance.
Like "Adventures in Stochastic Processes," Resnick s related and
very successful textbook, "A Probability Path" is rich in
appropriate examples, illustrations and problems and is suitable
for classroom use or self-study. The present uncorrected, softcover
reprintis designed to make this classic textbookavailable to a
wider audience.
"This book is different from the classical textbooks on
probability theory in that it treats the measure theoretic
background not as a prerequisite but as an integral part of
probability theory. The result is that the reader gets a thorough
and well-structured framework needed to understand the deeper
concepts of current day advanced probability as it is used in
statistics, engineering, biology and finance.... The pace of the
book is quick and disciplined. Yet there are ample examples
sprinkled over the entire book and each chapter finishes with a
wealthy section of inspiring problems. "
Publications of the International Statistical Institute
"This textbook offers material for a one-semester course in
probability, addressed to students whose primary focus is not
necessarily mathematics.... Each chapter is completed by an
exercises section. Carefully selected examples enlighten the reader
in many situations. The book is an excellent introduction to
probability and its applications. "
Revue Roumaine de Mathematiques Pures et Appliquees"
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