On Statistical Models for d‐Dimensional Stable Processes, and Some Generalizations

In statistical models where jumps of a d‐dimensional stable process (St)t≥0 are observed in windows with certain asymptotic properties, and where parameters appearing in the Levy measure of S are to be estimated, we have asymptotically efficient estimators. If Poisson random measure μ on (0, ∞) × (Rd\{0}) with intensity dtΛ(dx) replaces the jump measure of S, where Λ is a ε‐finite measure on Rd\{0} admitting tail parameters in a suitable sense, we specify a notion of neighbourhood which allows to treat efficiency in statistical experiments of the second type by switching to accompanying sequences of the stable process type considered first.