THEORY OF STOCHASTIC OBJECTS: PROBABILITY STOCHASTIC PROCESSES AND INFERENCE

Summary This book defines and investigates the concept of a random object. To accomplish this task naturally, it brings together three major areas; statistical inference, measure-theoretic probability theory, and stochastic processes. This point of view has not been explored by existing textbooks; one would need material on real analysis, measure and probability theory, as well as stochastic processes – in addition to at least one text on statistics- to capture the detail and depth of material that has gone into this volume. Presents and illustrates ‘random objects’ in different contexts, under a unified framework, starting with rudimentary results on random variables and random sequences, all the way up to stochastic partial differential equations. Reviews rudimentary probability and introduces statistical inference, from basic to advanced, thus making the transition from basic statistical modeling and estimation to advanced topics more natural and concrete.