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Hausdorff Measure for a Stable-Like Process over an Infinite Extension of a Local Field

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  • Anatoly N. Kochubei

    (Institute of Mathematics)

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.

Suggested Citation

  • Anatoly N. Kochubei, 2002. "Hausdorff Measure for a Stable-Like Process over an Infinite Extension of a Local Field," Journal of Theoretical Probability, Springer, vol. 15(4), pages 951-972, October.
    • Handle: RePEc:spr:jotpro:v:15:y:2002:i:4:d:10.1023_a:1020789821275
    DOI: 10.1023/A:1020789821275
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