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pro vyhledávání: '"Cruzeiro, Ana Bela"'
We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We show that the value process is the unique solution of this equation, in
Externí odkaz:
http://arxiv.org/abs/2301.09214
In this paper we introduce a class of forward-backward stochastic differential equations on tensor fields of Riemannian manifolds, which are related to semi-linear parabolic partial differential equations on tensor fields. Moreover, we will use these
Externí odkaz:
http://arxiv.org/abs/2301.06490
In this paper we consider the following non-linear stochastic partial differential equation (SPDE): \begin{align*} \begin{cases} \mathrm{d}u(s,x)=\sum^n_{i=1} \mathscr{L}_i u(s,x)\circ \mathrm{d}W_i(s)+\left(V(x)+\mu\Delta u(s,x)-\frac{1}{2}\vert\nab
Externí odkaz:
http://arxiv.org/abs/2209.06660
We describe, in an intrinsic way and using the global chart provided by Ito's parallel transport, a generalisation of the notion of geodesic (as critical path of an energy functional) to diffusion processes on Riemannian manifolds. These stochastic p
Externí odkaz:
http://arxiv.org/abs/2007.05291
We present a pair of adjoint optimal control problems characterizing a class of time-symmetric stochastic processes defined on random time intervals. The associated PDEs are of free-boundary type. The particularity of our approach is that it involves
Externí odkaz:
http://arxiv.org/abs/2007.02110
Akademický článek
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Autor:
Cruzeiro, Ana Bela
We show that the Navier-Stokes as well as a random perturbation of this equation can be derived from a stochastic variational principle where the pressure is introduced as a Lagrange multiplier. Moreover we describe how to obtain corresponding consta
Externí odkaz:
http://arxiv.org/abs/1807.01550
Publikováno v:
Potential Anal. 54 (2021) pp. 607-626
We consider a modified Euler equation on $\mathbb R^2$. We prove existence of weak global solutions for bounded (and fast decreasing at infinity) initial conditions and construct Gibbs-type measures on function spaces which are quasi-invariant for th
Externí odkaz:
http://arxiv.org/abs/1711.09045
Publikováno v:
Annales de l'Institut Henri Poincar\'e Probab. Statist. 56(3), 2211-2235, (2020)
In view of studying incompressible inviscid fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of inviscid fluids, the present paper is devoted to incompressible viscid fluids. A natura
Externí odkaz:
http://arxiv.org/abs/1704.02126
We construct Gaussian invariant measures for the two-dimensional Euler equation on the plane. We show the existence of solution with initial conditions in the support of the measures, namely $H^\beta_{loc}(\R^2)$ with $\beta<-1$. Uniqueness and conti
Externí odkaz:
http://arxiv.org/abs/1612.08587