Invariant Extensions of Positive Operators.
Sur l'existence d'une plus petite sous-tribu exhaustive par paire
Strong continuity of invariant probability charges
Consider a semigroup action on a set. We derive conditions, in terms of the induced action of the semigroup on {0,1}-valued probability charges, which ensure that all invariant probability charges are strongly continuous.
Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces
We describe quantization designs which lead to asymptotically and order optimal functional quantizers for Gaussian processes in a Hilbert space setting. Regular variation of the eigenvalues of the covariance operator plays a crucial role to achieve these rates. For the development of a constructive quantization scheme we rely on the knowledge of the eigenvectors of the covariance operator in order to transform the problem into a finite dimensional quantization problem of normal distributions. ...
Distortion mismatch in the quantization of probability measures
We elucidate the asymptotics of the -quantization error induced by a sequence of -optimal -quantizers of a probability distribution on when . In particular we show that under natural assumptions, the optimal rate is preserved as long as (and for every in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based cubature formulae in numerical integration on and on the Wiener space.
Moment estimates for Lev́y processes.
Expansions for Gaussian processes and Parseval frames.
A constructive sharp approach to functional quantization of stochastic processes.
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