Zobrazeno 1 - 10
of 103
pro vyhledávání: '"Martini, Mattia"'
In this work we study how diffusion-based generative models produce high-dimensional data, such as an image, by implicitly relying on a manifestation of a low-dimensional set of latent abstractions, that guide the generative process. We present a nov
Externí odkaz:
http://arxiv.org/abs/2410.03368
Quantitative convergence for mean field control with common noise and degenerate idiosyncratic noise
We consider the convergence problem in the setting of mean field control with common noise and degenerate idiosyncratic noise. Our main results establish a rate of convergence of the finite-dimensional value functions $V^N$ towards the mean field val
Externí odkaz:
http://arxiv.org/abs/2409.14053
Autor:
Delarue, François, Martini, Mattia
The purpose of this work is to provide a finite dimensional approximation of the solution to a mean field optimal control problem set on the $d$-dimensional torus. The approximation is obtained by means of a Fourier-Galerkin method, the main principl
Externí odkaz:
http://arxiv.org/abs/2403.15642
Autor:
Cosso, Andrea, Martini, Mattia
Publikováno v:
Electron. Commun. Probab. 28: 1-11 (2023)
In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are able to cons
Externí odkaz:
http://arxiv.org/abs/2303.15160
Autor:
Djehiche, Boualem, Martini, Mattia
Publikováno v:
Vol. 528, Issue 1, 2023
We provide a characterization of an optimal stopping time for a class of finite horizon time-inconsistent optimal stopping problems (OSPs) of mean-field type, adapted to the Brownian filtration, including those related to mean-field diffusion process
Externí odkaz:
http://arxiv.org/abs/2209.04174
Publikováno v:
Employee Relations: The International Journal, 2023, Vol. 45, Issue 7, pp. 79-102.
Externí odkaz:
http://www.emeraldinsight.com/doi/10.1108/ER-02-2022-0072
Autor:
Martini, Mattia
We study the backward Kolmogorov equation on the space of probability measures associated to the Kushner-Stratonovich equation of nonlinear filtering. We prove existence and uniqueness in the viscosity sense and, in particular, we provide a compariso
Externí odkaz:
http://arxiv.org/abs/2202.11072
Autor:
Martini, Mattia
Publikováno v:
Stochastic Processes and their Applications, 161, 2023
We introduce and study some backward Kolmogorov equations associated to stochastic filtering problems. Measure-valued processed arise naturally in the context of stochastic filtering and one can formulate two stochastic differential equations, called
Externí odkaz:
http://arxiv.org/abs/2107.11865
Autor:
Djehiche, Boualem, Martini, Mattia
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 December 2023 528(1)