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Giovedì 18 Dicembre, ore 11:00
Aula Dottorato, Dipartimento di Matematica, Universita' degli Studi di Milano
via C. Saldini 50, Milano

BRUNO GALERNE 
(MAP5, Université Paris Descartes) 

terrà un seminario dal titolo

Random Fields of Bounded Variation and Computation of their Variation Intensity

ABSTRACT:
The purpose of this talk is to define and characterize random fields of bounded variation, that is random fields with sample paths in the space of functions of bounded variation, and to study their mean total variation. We will mainly focus on the mean variation of random fields with stationary increments. We will show that this mean variation is proportional to the Lebesgue measure, and an expression of the constant of proportionality, called the variation intensity, will be established. This expression shows in particular that the variation intensity only depends on the family of two-dimensional distributions of the stationary increment random field.
When restricting to random sets, the obtained results give generalizations of well-known formulas from stochastic geometry and mathematical morphology. The interest of these general results will be illustrated by computing the variation intensities of several classical stationary random field and random set models, namely Gaussian random fields and excursion sets, Poisson shot noises, Boolean models, dead leaves models, and random tessellations.

Tutti gli interessati sono invitati a partecipare.

Saluti
Elena Villa