Hölder Continuity of Random Processes
Witold Bednorz ()
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Witold Bednorz: University of Warsaw
Journal of Theoretical Probability, 2007, vol. 20, issue 4, 917-934
Abstract:
Abstract For a Young function φ and a Borel probability measure m on a compact metric space (T,d) the minorizing metric is defined by $$\tau_{m,\varphi}(s,t):=\max\biggl\{\int^{d(s,t)}_{0}\varphi^{-1}\biggl(\frac{1}{m(B(s,\varepsilon))}\biggr)d\varepsilon,\int^{d(s,t)}_{0}\varphi^{-1}\biggl(\frac{1}{m(B(t,\varepsilon ))}\biggr)d\varepsilon\biggr\}.$$ In the paper we extend the result of Kwapien and Rosinski (Progr. Probab. 58, 155–163, 2004) relaxing the conditions on φ under which there exists a constant K such that $$\mathbf{E}\sup_{s,t\in T}\varphi\biggl(\frac{|X(s)-X(t)|}{K\tau _{m,\varphi}(s,t)}\biggr)\leq 1,$$ for each separable process X(t), t∈T which satisfies $\sup_{s,t\in T}\mathbf{E}\varphi(\frac {|X(s)-f(t)|}{d(s,t)})\leq 1$ . In the case of φ p (x)≡x p , p≥1 we obtain the somewhat weaker results.
Keywords: Majorizing measures; Minorizing metric; Regularity of samples (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10959-007-0094-x
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