Law of large numbers and ergodic theorem for convex weak star compact valued Gelfand-integrable mappings

Jérôme Dedecker (1) , Clémentine Prieur (2) , Paul Raynaud de Fitte (3)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 LSP - Laboratoire de Statistique et Probabilités
3 LMRS - Laboratoire de Mathématiques Raphaël Salem

We prove several results in the integration of convex weak star (resp.~norm compact) valued random sets with application to weak star Kuratowski convergence in the law of largenumbers for convex norm compact valued Gelfand-integrable mappings in the dual of a separable Banach space. We also establish several weak star Kuratowski convergence in the law of large numbers and ergodic theorem involving the subdifferential operators of Lipschitzean functions defined on a separable Banach space, and also provide an application to a closure type result arisen in evolution inclusions.

Mots clés: Conditional expectation; subdifferential; generalized directional derivative; locally Lipschitzean; Haar measure; law of large numbers; ergodic

Domaines: Probabilités [math.PR]

Jérôme Dedecker, Clémentine Prieur, Paul Raynaud de Fitte. Law of large numbers and ergodic theorem for convex weak star compact valued Gelfand-integrable mappings. Advances in mathematical economics, 17, Springer, pp.1-37, 2013, 978-4-431-54323-7; 978-4-431-54324-4. ⟨10.1007/978-4-431-54324-4_1⟩. ⟨hal-00726650⟩