Dissipative and totally dissipative evolutions in Wasserstein spaces
speaker: Giulia Cavagnari (Politecnico di Milano)abstract: We study well-posedness and probabilistic representation for first-order evolution equations in Wasserstein spaces driven by probability vector fields. Mimicking the classical theory in Hilbert spaces, we give a metric notion of dissipativity providing existence and uniqueness using an explicit Euler scheme. We study also an implicit Euler scheme under lifting technique over a space of parametrizations. In this case, the dissipativity of the lifted operator corresponds to a stronger notion of total dissipativity in the measure-theoretic framework. When the dissipative vector field has a totally dissipative barycenter, we compare the two approaches also at the level of the probabilistic representations. This is a joint work with Giuseppe Savaré (Bocconi University - Italy) and Giacomo Enrico Sodini (University of Vienna - Austria).
timetable:
Mon 2 Dec, 17:00 - 17:30, Aula Dini
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