Operator self-similar processes on Banach spaces
The authors investigate operator self-similar processes (OSS) on a Banach space \(E\) using the theory of one-parameter groups of operators on \(E\). One of the main results claims that if \(\{ X(t) : t>0 \}\) is OSS and if \(\text{Span}(EX(t) : t>0) = E\), then its scaling family of operators is a uniquely determined multiplicative group. Moreover, if \(EX(t)\) is continuous and \(\text{Span}(EX(t): t>0)\) is a subset having category 2 (in the sense of Baire), then \(EX(t)\) has a power-growth with exponent \(a\geq 0\).
scientific article; zbMATH DE number 5134593
scientific article