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

On level and collision sets of some Feller processes