ABSTRACT
This chapter discusses the foundation of stochastic processes. Much of statistical analysis is concerned with models in which the observations are assumed to vary independently. However, a great deal of data in economics, finance, engineering, and the natural sciences occur in the form of time series where observations are dependent and where the nature of the dependence is of interest in itself. The chapter provides a modern introduction to stochastic processes. Because statistical analysis for stochastic processes largely relies on asymptotic theory, the chapter explains some useful limit theorems and central limit theorems. In statistical asymptotic theory, it is known that one of the most fundamental quantities becomes a martingale under suitable conditions. If the statistical average of the process equals the time average, the process will be called ergodic.
