ON SELF-SIMILAR STOCHASTIC INTEGRAL PROCESSES

A stochastics process $X = {X(t) : t \in T}$, with an index set T, is said to be infinitely divisible (ID) if its finite dimensional distributions are all ID. An ID process X is said to be a stochastic integral process if $X = {X(t) : t \in T} =^D {\int f_td\Lambda : t \in T}$ where $f : T \times S \to R$ is a deterministic function and $\Lambda$ is an ID random measure on a $\delta$-ring S of subsets of an arbitrary non-empty set S with the property; there exists an increasing sequence ${S_n}$ of sets in S with $U_n S_n = S$. Here $=^D$ denotes equality in all finite dimensional distributions.