Many probability 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 reprint is designed
to make this classic textbook available 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 itis 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 Mathématiques Pures et Appliquées
Les mer
Produktdetaljer
ISBN
9780817684099
Publisert
2018
Utgiver
Springer Nature
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter