ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book introduces point processes and their distributional theory. It discusses some detail the kinds of problems of statistical inference and state estimation. The book addresses distribution-based inference using empirical estimators, with focuses on large-sample properties, corresponding to observation of independent realizations. It presents an analogously broad description of intensity-based inference for point processes on the line. The book describes important special classes of point processes — Poisson processes, Cox processes, renewal processes and stationary point processes. Renewal processes are significant because many stochastic processes contain embedded renewal processes, whose points typically are times at which the underlying process renews itself probabilistically. Important properties of renewal processes are of two types: those associated with the renewal equation and asymptotic properties following from the renewal theorem.
