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The Hölder continuity of Westwater process and its applications

The Hölder continuity of Westwater process and its applications In this paper, the Hölder continuity of Westwater processX t is concerned. More precisely, we show that there exists a random variableτ C ∈ (0, ∞) for anyC ∈ (3, ∞) such that $$|X_s - X_t | \leqslant C\sqrt {|s - t||\log |t - s||,} \forall |t - s|< \tau _c .$$ As its applications, we give two bounds respectively for the Hausdorff measure function of multiple time set of Westwater process, and the Hausdorff measure of the imageX(E) of a Borel setE by Westwater process. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

The Hölder continuity of Westwater process and its applications

Acta Mathematicae Applicatae Sinica , Volume 7 (4) – Jul 14, 2005

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Publisher
Springer Journals
Copyright
Copyright © 1991 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02009681
Publisher site
See Article on Publisher Site

Abstract

In this paper, the Hölder continuity of Westwater processX t is concerned. More precisely, we show that there exists a random variableτ C ∈ (0, ∞) for anyC ∈ (3, ∞) such that $$|X_s - X_t | \leqslant C\sqrt {|s - t||\log |t - s||,} \forall |t - s|< \tau _c .$$ As its applications, we give two bounds respectively for the Hausdorff measure function of multiple time set of Westwater process, and the Hausdorff measure of the imageX(E) of a Borel setE by Westwater process.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 14, 2005

References