Prediction theory in continuous time

TL;DR

This paper reviews classical prediction theory for stationary continuous-time stochastic processes, emphasizing simple proofs that clarify the probabilistic interpretation of known results.

Contribution

It provides concise, accessible proofs of classical prediction results in continuous time, highlighting their probabilistic significance.

Findings

Classical solutions for infinite and finite past prediction problems are summarized.

The paper offers simplified proofs that enhance understanding of the probabilistic meaning.

It clarifies the theoretical foundations of prediction in continuous-time stochastic processes.

Abstract

We consider prediction theory for stationary stochastic processes in continuous time. We discuss prediction using the whole (infinite) past, and using only a finite section of the past. The solutions to both these classical problems have long been known. Our focus is to provide short simple proofs which reveal the probabilistic meaning of the results.