Carlo Pucci, mathematician and citizen

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STABLE LAWS ARISING FROM HITTING DISTRIBUTIONS OF PROCESSES ON HOMOGENEOUS TREES AND THE HYPERBOLIC HALF-PLANE

The projective line with respect to a local field is the boundary of the Bruhat-Tits tree associated to the field, much in the same way as the realprojective line is the boundary of the upper half-plane. In both cases we may consider the horocycles with respect to the point at infinity. These horocycles are exactly the horizontal lines {y = a} with a>0 in the real case, while in the case of a local field the horocycles may be thought of as discretizations of the field obtained by collapsing to a point each ball of a given radius. In this paper we exploit this geometric parallelism to construct symmetric α-stable random variables on the real line and on a local field by completely analogous procedures. In the case of a local field the main ingredient is a drifted random walk on the tree. In the real case the random walk is replaced by a drifted Brownian motion on the hyperbolic halfplane

Non-symmetric hitting distributions on the hyperbolic half-plane and subordinated perpetuities

We study the law of functionals whose prototype is ?0+8 eBs(?) dWs(µ), where B(?) and W(µ) are independent Brownian motions with drift. These functionals appear naturally in risk theory as well as in the study of in variant diffusions on the hyperbolic half-plane. Emphasis is put on the fact that the results are obtained in two independent, very different fashions (invariant diffusions on the hyperbolic half-plane and Bessel processes)

Decomposition of variance in terms of conditional means

Two different sets of data are used to test an apparently new approach to the analysis of the variance of a numerical variable which depends on qualitative variables. We suggest that this approach be used to complement other existing techniques to study the interdependence of the variables involved. According to our method, the variance is expressed as a sum of orthogonal components, obtained as differences of conditional means, with respect to the qualitative characters. The resulting expression for the variance depends on the ordering in which the characters are considered. We suggest an algorithm which leads to an ordering which is deemed natural. The first set of data concerns the score achieved by a population of students on an entrance examination based on a multiple choice test with 30 questions. In this case the qualitative characters are dyadic and correspond to correct or incorrect answer to each question. The second set of data concerns the delay to obtain the degree for a population of graduates of Italian universities. The variance in this case is analyzed with respect to a set of seven specific qualitative characters of the population studied (gender, previous education, working condition, parent's educational level, field of study, etc.)