CONTENTS Introduction......................................................................................................................................... 5 I. Prediction of strictly stationary random fields.................................................................................... 6 II. Prediction of stationary-in-norm fields in Banach spaces of random variables........................ 23 § 1. Banach spaces of random variables................................................................................ 23 § 2. Prediction of stationary-in-norm sequences of random variables.............................. 25 § 3. Markov optimization property of stationary-in-norm sequences................................... 28 § 4. Definition of a stationary-in-norm random field admitting a prediction....................... 37 § 5. Decomposition Theorem..................................................................................................... 39 § 6. Stochastic measures........................................................................................................... 40 § 7. Completely non-deterministic random fields................................................................. 52 III. Prediction of strictly stationary random fields on groups.............................................................. 60 References................................................................................................................................................. 69