Small ball estimates in \(p\)-variation for stable processes
A general estimate is derived for the strong \(p\)-variation of a strictly stable process with index \(\alpha \in (0, 2)\). Several special cases are treated in detail, and four theorems are established. A few section headings may give an impression of the rich contents of the paper. 2.1: Strictly stable processes and their strong \(p\)-variation. 2.2: The case when \(| Z| \) is a subordinator or \(p \leq 1\). 2.3: The case when \(| Z| \) is not a subordinator and \(p > 1\). 6: General stable processes. 6.2: More on the small ball constant in the symmetric case. 6.3: Some other two-sided estimates in the symmetric case. 6.4: A lower estimate on the Hölder small ball constant for Brownian motion.
scientific article; zbMATH DE number 2153676