New spaces for the convergence of partial sum processes with clustering

speaker: Mike Todd (University of St Andrews )

abstract: Functional limit theorems in dynamical systems come from summing observations along orbits. If the observable has finite second moment, and the dynamical system is sufficiently hyperbolic, then the (suitably scaled) limit is a Brownian motion in path space. We are interested in the infinite second moment case, where the heavy tails mean that there are big jumps in the sums which mean that limits are expected to be Lévy processes. In this talk I will discuss topologies for convergence: in the case of clusters of jumps, we find a space which captures the sizes and (sequential) orders of all of these jumps. This is joint work with Ana Cristina Freitas and Jorge Freitas.

timetable:
Wed 31 May, 10:10 - 11:00, Aula Dini
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