Hölder continuity of random processes
نویسنده
چکیده
For a Young function ϕ and a Borel probability measure m on a compact metric space (T, d) the minorizing metric is defined by τ m,ϕ (s, t) := max{ d(s,t) 0 ϕ −1 (1 m(B(s, ε)))dε, d(s,t) 0 ϕ −1 (1 m(B(t, ε)))dε}. In the paper we extend the result of Kwapien and Rosinski [2] relaxing the conditions on ϕ under which there exists a constant K such that E sup s,t∈T ϕ(|X(s) − X(t)| Kτ m,ϕ (s, t)) 1, for each separable process X(t), t ∈ T which satisfies sup s,t∈T Eϕ(|X(s)−f (t)| d(s,t)) 1. In the case of ϕ p (x) ≡ x p , p 1 we obtain the somewhat weaker results.
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Sample Hölder continuity of stochastic processes and majorizing measures
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تاریخ انتشار 2007