A representation of infinitely divisible signed random measures.
Invariance principles in
An invariance principle in for non stationary -mixing sequences
Invariance principle in is studied using signed random measures. This approach to the problem uses an explicit isometry between and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a version of the invariance principle in the case of -mixing random variables. Our result is not available in the -setting.
Mean quadratic convergence of signed random measures
We consider signed Radon random measures on a separable, complete and locally compact metric space and study mean quadratic convergence with respect to vague topology on the space of measures. We prove sufficient conditions in order to obtain mean quadratic convergence. These results are based on some identification properties of signed Radon measures on the product space, also proved in this paper.
On the conditional intensity of a random measure
We prove the existence of the conditional intensity of a random measure that is absolutely continuous with respect to its mean; when there exists an L-intensity, , the conditional intensity is obtained at the same time almost surely and in the mean.
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