Books like An introduction to probability theory and its applications by William Feller

A concise primer on probability theory and stochastic models for science, engineering, economics and related disciplines.

A comprehensive, self-contained, yet easily accessible presentation of basic concepts, examining measure-theoretic foundations as well as analytical tools. Covers classical as well as modern methods, with emphasis on the strong interrelationship between probability theory and mathematical analysis, and with special stress on the applications to statistics and analysis. Includes recent developments, numerous examples and remarks, and various end-of-chapter problems. Notes and comments at the end of each chapter provide valuable references to sources and to additional reading material.

Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory. Like the previous editions, this new edition will be well received by students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory. --back cover

A comprehensive introduction to machine learning, combining breadth and depth, and written in an informal, accessible style with pseudo-code for algorithms.

This book is an advanced text on probability theory. By presupposing the background of a standard first course in real analysis and a 'soft' course in probability theory, it gives a compact treatment of several key topics in probability, selected on the basis of their importance in forming the foundations of the modern theory of stochastic processes. It is ideal for graduate students and researchers in probability theory and stochastic processes and their applications. It is also well suited for scientists in allied fields such as mathematical statistics/ economics/physics, electrical engineering, operations research who wish to augment their background in probability theory.

A concise, practical introduction to probability and statistical theory tailored for economists, covering essential concepts and methods in econometrics.