Leírás
SZTE, TTIK, Bolyai Intézet, Sztochasztika szeminárium
Abstract. We consider sample path properties of the solution to the stochastic heat equation driven by a Lévy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solution is shown to have a càdlàg modification in fractional Sobolev spaces of index less than -d/2. Concerning the partial regularity of the solution in time or space when the other variable is fixed, we determine critical values for the Blumenthal-Getoor index of the Lévy noise such that noises with a smaller index entail continuous sample paths, while Lévy noises with a larger index entail sample paths that are unbounded on any non-empty open subset.
This is joint work with Thomas Humeau and Robert Dalang (EPFL).