Dipartimento di Matematica, Sapienza Università di Roma
Martedì 15 novembre
Ore 14:00, Aula di Consiglio
Seminario di Probabilità e Statistica Matematica
Random dynamical systems: contraction and recurrence propertie
Marc Peigné, Université de Tours
Abstract: Consider a proper metric space X and a sequence (Fn) of i.i.d.
random continuous mappings X → X. It induces the stochastic dynamical
system (SDS)
Xn = Fn ◦ · · · ◦ F1(x) starting at x ∈ X.
We study existence and uniqueness of invariant measures, under some
assumptions of
contraction on the Fn, as well as recurrence and ergodicity of this process.
We will consider two main examples: the case where the Fn are affine maps
of the real line
and the case where Xn is the reflected random walk on the positive real
line.
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