- 1997 (3) (entfernen)
- In an autonomous Markovian dynamical system a discrete measure could be transformed into an absolutely countinuous distribution in finite time even if the system has locally unique solutions except for countably many initial states (1997)
- In this note, answering a question of N. Maslova, we give a two-dimensional elementary example of the phenomenon indicated in the title. Perhaps this simple example may serve as an object of comparison for more refined models like in the theory of kinetic differential equations where similar questions still seem to be unsettled.
- On Risk Rates and Large Deviations in Finite Markov Chain Experiments (1997)
- The observation of an ergodic Markov chain asymptotically allows perfect identification of the transition matrix. In this paper we determine the rate of the information contained in the first n observations, provided the unknown transition matrix belongs to a known finite set. As an essential tool we prove new refinements of the large deviation theory of the empirical pair measure of finite Markov chains. Keywords: Markov Chain, Entropy, Bayes risk, Large Deviations.
- Sudakov's typical marginals, random linear functionals and a conditional central limit theorem (1997)
- V.N. Sudakov [Sud78] proved that the one-dimensional marginals of a highdimensional second order measure are close to each other in most directions. Extending this and a related result in the context of projection pursuit of P. Diaconis and D. Freedman [Dia84], we give for a probability measure P and a random (a.s.) linear functional F on a Hilbert space simple sufficient conditions under which most of the one-dimensional images of P under F are close to their canonical mixture which turns out to be almost a mixed normal distribution. Using the concept of approximate conditioning we deduce a conditional central limit theorem (theorem 3) for random averages of triangular arrays of random variables which satisfy only fairly weak asymptotic orthogonality conditions.