Central Limit Theorem in Holder spaces in the terms of majorizing measures

Abstract

We obtain some sufficient conditions for the Central Limit Theorem for the random processes (fields) with values in the separable part of Holder space in the modern terms of majorizing (minorizing) measures, belonging to X.Fernique and M.Talagrand. We introduce a new class of Banach spaces-rectangle Holder spaces and investigate CLT in this spaces via the fractional order Sobolev-Grand Lebesgue norms. Our further considerations based on the improvement of the L.Arnold and P.Imkeller generalization of the classical Garsia-Rodemich-Rumsey inequality, which allow us to reduce degree of the distance in the important particular cases.