Random Markov-self-similar measures. (Q1766057)

Self-similar fractal sets in the Euclidean space are usually constructed by applying iteratively a fixed finite family of contractive mappings to a given initial set. Random self-similar sets are obtained if the contractive mappings are chosen randomly and independently at each step, following a prescribed distribution. The concept of a random Markov-self-similar set is a further generalization, where a Markov chain with finitely many states rules the choice of the contractions at each step. The author introduces in a natural way random Markov-self-similar measures as certain random measures supported by these sets and proves their existence and self-similarity properties.