On level and collision sets of some Feller processes

Victoria Knopova; René L. Schilling

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arXiv · 1412.8726

On level and collision sets of some Feller processes

Victoria Knopova·René L. Schilling

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Abstract

This paper is about lower and upper bounds for the Hausdorff dimension of the level and collision sets of a class of Feller processes. Our approach is motivated by analogous results for L\'evy processes by Hawkes (for level sets), Taylor and Jain & Pruitt (for collision sets). Since Feller processes lack independent or stationary increments, the methods developed for L\'evy processes cannot be used in a straightforward manner. Under the assumption that the Feller process possesses a transition probability density, which admits lower and upper bounds of a certain type, we derive sufficient conditions for regularity and non-polarity of points; together with suitable time changes this allows us to get upper and lower bounds for the Hausdorff dimension.

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Victoria Knopova, René L. Schilling. 2014-12-30. On level and collision sets of some Feller processes. https://arxiv.org/abs/1412.8726

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