Multivariate empirical characteristic functions

Abstract

and specifically EYv(t ) Yv(s) = C(t-s)-C(t) C(-s).Just like in the univariate case ([17], [5], [26]), the finite-dimensional distributions of Y, converge by the multidimensional central limit theorem to those of Yr.But Y, does not always converge weakly in cg(S) to YF, since the latter process can be almost surely discontinuous for certain F's.When looking at these kind of properties of the Yr process, the following stochastic integral representation is useful.

Locations

• Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete - View - PDF