Chapter 12 - Sequential Inference for Stochastic Processes

Abstract

This chapter discusses inference procedures for stochastic processes through sequential procedures. Sequential procedure is a method of statistical inference whose characteristic feature is that the number of observations required or the time required for observation of the process is not determined in advance. The decision to terminate the observation on the process depends, at each stage, on the results of the observations previously made. A merit of the sequential method is that test procedures and estimation procedures can be derived, which require on the average, a substantially smaller time period of observation or smaller number of observations than equally reliable procedures based on a predetermined time of observation or number of observations, respectively. The chapter also discusses sequential estimation for processes with continuous parameters. It reviews efficient sequential estimation for stationary processes with independent increments. It presents some results on Wald's equation in continuous time and sequential probability ratios tests for stationary processes with independent increments and for continuous time Markov processes.