We introduce a new notion of irregularity of paths, in terms of control of growth of the size of small balls by means of the occupation measure of the path. This notion ensures Besov regularity of the occupation measure and thus extends the analysis of Catellier and Gubinelli [1] to general Besov spaces. On stochastic processes this notion is granted by suitable properties of local non-determinism.
Yet another notion of irregularity through small ball estimates
Marco Romito;Leonardo Tolomeo
2026-01-01
Abstract
We introduce a new notion of irregularity of paths, in terms of control of growth of the size of small balls by means of the occupation measure of the path. This notion ensures Besov regularity of the occupation measure and thus extends the analysis of Catellier and Gubinelli [1] to general Besov spaces. On stochastic processes this notion is granted by suitable properties of local non-determinism.File in questo prodotto:
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