Hausdorff Measure for a Stable-Like Process over an Infinite Extension of a Local Field |
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Authors: | Anatoly N Kochubei |
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Institution: | (1) National Academy of Sciences of Ukraine, Institute of Mathematics, Tereshchenkivska 3, Kiev, 01601, Ukraine |
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Abstract: | We consider an infinite extension K of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. K is equipped with an inductive limit topology; its conjugate K is a completion of K with respect to a topology given by certain explicitly written seminorms. The semigroup of measures, which defines a stable-like process X(t) on K, is concentrated on a compact subgroup S K. We study properties of the process X
S
(t), a part of X(t) in S. It is shown that the Hausdorff and packing dimensions of the image of an interval equal 0 almost surely. In the case of tamely ramified extensions a correct Hausdorff measure for this set is found. |
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Keywords: | Stable process local field tamely ramified extension Hausdorff dimension Hausdorff measure |
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