Page 570 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 570
STOCHASTIC EVOLUTION EQUATIONS (MS-68)
mean. Such deviations, though rare, can have significant consequences—such as a concentra-
tion of energy or the appearance of a vacuum—which make them important to understand and
simulate.
In this talk, which is based on joint work with Benjamin Gess, I will introduce a continuum
model for simulating rare events in the zero range and symmetric simple exclusion process. The
model is based on an approximating sequence of stochastic partial differential equations with
nonlinear, conservative noise. The solutions capture to first-order the central limit fluctuations
of the particle system, and they correctly simulate rare events in terms of a large deviations
principle.
Invariant measures for 2D inviscid fluids with linear damping and
stochastic forcing term
Benedetta Ferrario, benedetta.ferrario@unipv.it
Università di Pavia, Italy
Coauthor: Hakima Bessaih
We study the two-dimensional Euler equations, damped by a linear term and driven by an ad-
ditive noise. We prove existence of an invariant measure in the space L∞, where the problem
has a unique global solution. This requires to deal with the weak-∗ topology and the associated
Markov semigroup is proven to be sequentially weakly Feller.
Singular quasilinear SPDEs
Máté Gerencsér, mgerencs@tuwien.ac.at
TU Vienna, Austria
We overview some recent results on quasilinear stochastic PDEs. The developments for fully
parabolic (nondegenerate) equations have led to expansions of the theories of regularity struc-
tures and paracontrolled distributions, as well as to some unexpected connections to renormal-
isation symmetries. On the other hand, degenerate equations are far less understood, and even
for equations with an Itô structure often only martingale solutions are available, natural unique-
ness questions are still open. Based on joint works with Y. Bruned, K. Dareiotis, B. Gess, M.
Hairer.
Optimal control of path-dependent McKean-Vlasov SDEs in infinite
dimension
Fausto Gozzi, fgozzi@luiss.it
Luiss University, Italy
Coauthors: Andrea Cosso, Idris Kharroubi, Huyen Pham, Mauro Rosestolato
We study the optimal control of path-dependent McKean-Vlasov equations valued in Hilbert
spaces motivated by non Markovian mean-field models driven by stochastic PDEs. We first
establish the well-posedness of the state equation, and then we prove the dynamic program-
ming principle (DPP) in such a general framework. The crucial law invariance property of the
568
mean. Such deviations, though rare, can have significant consequences—such as a concentra-
tion of energy or the appearance of a vacuum—which make them important to understand and
simulate.
In this talk, which is based on joint work with Benjamin Gess, I will introduce a continuum
model for simulating rare events in the zero range and symmetric simple exclusion process. The
model is based on an approximating sequence of stochastic partial differential equations with
nonlinear, conservative noise. The solutions capture to first-order the central limit fluctuations
of the particle system, and they correctly simulate rare events in terms of a large deviations
principle.
Invariant measures for 2D inviscid fluids with linear damping and
stochastic forcing term
Benedetta Ferrario, benedetta.ferrario@unipv.it
Università di Pavia, Italy
Coauthor: Hakima Bessaih
We study the two-dimensional Euler equations, damped by a linear term and driven by an ad-
ditive noise. We prove existence of an invariant measure in the space L∞, where the problem
has a unique global solution. This requires to deal with the weak-∗ topology and the associated
Markov semigroup is proven to be sequentially weakly Feller.
Singular quasilinear SPDEs
Máté Gerencsér, mgerencs@tuwien.ac.at
TU Vienna, Austria
We overview some recent results on quasilinear stochastic PDEs. The developments for fully
parabolic (nondegenerate) equations have led to expansions of the theories of regularity struc-
tures and paracontrolled distributions, as well as to some unexpected connections to renormal-
isation symmetries. On the other hand, degenerate equations are far less understood, and even
for equations with an Itô structure often only martingale solutions are available, natural unique-
ness questions are still open. Based on joint works with Y. Bruned, K. Dareiotis, B. Gess, M.
Hairer.
Optimal control of path-dependent McKean-Vlasov SDEs in infinite
dimension
Fausto Gozzi, fgozzi@luiss.it
Luiss University, Italy
Coauthors: Andrea Cosso, Idris Kharroubi, Huyen Pham, Mauro Rosestolato
We study the optimal control of path-dependent McKean-Vlasov equations valued in Hilbert
spaces motivated by non Markovian mean-field models driven by stochastic PDEs. We first
establish the well-posedness of the state equation, and then we prove the dynamic program-
ming principle (DPP) in such a general framework. The crucial law invariance property of the
568
