Prediction theory in continuous time

2021/11/16 by Ν. H. Bingham, Bingham, N. H.
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Mathematics #Primary 60-02 Secondary 62-02 #Probability (math.PR) #Statistical Mechanics and Entropy #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2111.08560

openalex publication_date 2021/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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