Stochastic extremal problems and the strong Markov property of random fields

CONTENTS Introduction § 1. Stochastic models § 2. The strong Markov property. Splitting random elements § 3. Extremal problems and splitting random sets § 4. Constructions of splitting elements based on the solution of extremal problems § 5. Random change of variables § 6. The strong Markov property of random fields on a Euclidean space § 7. Constructions of splitting domains § 8. Survey of examples and applications References