Page 573 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 573
STOCHASTIC EVOLUTION EQUATIONS (MS-68)
real-valued martingales.
In the present talk we will discuss the generalisation of local characteristics to Banach space-
valued martingales. In particular, we will prove sharp Lp estimates for tangent martingales with
values in infinite dimensions. This will help us to provide new sharp bounds for vector-valued
stochastic integrals with respect to a general martingale.
Invariant measures for a stochastic nonlinear and damped 2D
Schrödinger equation
Margherita Zanella, margherita.zanella@polimi.it
Politecnico di Milano, Italy
We consider a two-dimensional stochastic nonlinear defocusing Schrödinger equation with
zero-order linear damping, where the stochastic forcing term is given by a combination of a
linear multiplicative noise in Stratonovich form and a nonlinear noise in Itô form. We work at
the same time on compact Riemannian manifolds without boundary and on compact smooth
domains with either Dirichlet or Neumann boundary conditions. We construct a martingale
solution using a modified Faedo-Galerkin’s method, then by means of suitable Strichartz es-
timates we show the pathwise uniqueness of solutions. Finally, we prove the existence of in-
variant measures by means of a version of the Krylov-Bogoliubov method, which involves the
weak topology, as proposed by Maslowski and Seidler . Some remarks on the uniqueness in a
particular case are provided as well. The talk is based on a joint work with B. Ferrario and Z.
Brzez´niak.
571
real-valued martingales.
In the present talk we will discuss the generalisation of local characteristics to Banach space-
valued martingales. In particular, we will prove sharp Lp estimates for tangent martingales with
values in infinite dimensions. This will help us to provide new sharp bounds for vector-valued
stochastic integrals with respect to a general martingale.
Invariant measures for a stochastic nonlinear and damped 2D
Schrödinger equation
Margherita Zanella, margherita.zanella@polimi.it
Politecnico di Milano, Italy
We consider a two-dimensional stochastic nonlinear defocusing Schrödinger equation with
zero-order linear damping, where the stochastic forcing term is given by a combination of a
linear multiplicative noise in Stratonovich form and a nonlinear noise in Itô form. We work at
the same time on compact Riemannian manifolds without boundary and on compact smooth
domains with either Dirichlet or Neumann boundary conditions. We construct a martingale
solution using a modified Faedo-Galerkin’s method, then by means of suitable Strichartz es-
timates we show the pathwise uniqueness of solutions. Finally, we prove the existence of in-
variant measures by means of a version of the Krylov-Bogoliubov method, which involves the
weak topology, as proposed by Maslowski and Seidler . Some remarks on the uniqueness in a
particular case are provided as well. The talk is based on a joint work with B. Ferrario and Z.
Brzez´niak.
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