Zobrazeno 1 - 10
of 67
pro vyhledávání: '"Galimberti, Luca"'
Autor:
Galimberti, Luca
Leveraging the infinite dimensional neural network architecture we proposed in arXiv:2109.13512v4 and which can process inputs from Fr\'echet spaces, and using the universal approximation property shown therein, we now largely extend the scope of thi
Externí odkaz:
http://arxiv.org/abs/2406.09310
Predicting the conditional evolution of Volterra processes with stochastic volatility is a crucial challenge in mathematical finance. While deep neural network models offer promise in approximating the conditional law of such processes, their effecti
Externí odkaz:
http://arxiv.org/abs/2405.20094
We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa--Holm equation perturbed by a convective, position-dependent, noise term. We establish the first global-in-time existence result for dissipativ
Externí odkaz:
http://arxiv.org/abs/2211.07046
Causal operators (CO), such as various solution operators to stochastic differential equations, play a central role in contemporary stochastic analysis; however, there is still no canonical framework for designing Deep Learning (DL) models capable of
Externí odkaz:
http://arxiv.org/abs/2210.13300
We propose a new methodology for pricing options on flow forwards by applying infinite-dimensional neural networks. We recast the pricing problem as an optimization problem in a Hilbert space of real-valued function on the positive real line, which i
Externí odkaz:
http://arxiv.org/abs/2202.11606
We define a neural network in infinite dimensional spaces for which we can show the universal approximation property. Indeed, we derive approximation results for continuous functions from a Fr\'echet space $\X$ into a Banach space $\Y$. The approxima
Externí odkaz:
http://arxiv.org/abs/2109.13512
Autor:
Benth, Fred Espen, Galimberti, Luca
We provide a detailed analysis of the Gelfand integral on Fr\'echet spaces, showing among other things a Vitali theorem, dominated convergence and a Fubini result. Furthermore, the Gelfand integral commutes with linear operators. The Skorohod integra
Externí odkaz:
http://arxiv.org/abs/2103.08171
Autor:
Galimberti, Luca, Karlsen, Kenneth H.
We analyze continuity equations with Stratonovich stochasticity, $\partial \rho+ div_h \left[ \rho \circ\left(u(t,x)+\sum_{i=1}^N a_i(x) \dot W_i(t) \right) \right]=0$, defined on a smooth closed Riemannian manifold $M$ with metric $h$. The velocity
Externí odkaz:
http://arxiv.org/abs/2101.06934
Autor:
Galimberti, Luca, Karlsen, Kenneth H.
We consider the initial-value problem for stochastic continuity equations of the form $$ \partial_t \rho + \text{div}_h \left[\rho \left(u(t,x) + \sum_{i=1}^N a_i(x)\circ \frac{dW^i}{dt}\right)\right] = 0, $$ defined on a smooth closed Riemanian mani
Externí odkaz:
http://arxiv.org/abs/1912.10731
Autor:
Bottiroli, Maurizio, Calini, Angelo, Morici, Nuccia, Tavazzi, Guido, Galimberti, Luca, Facciorusso, Clorinda, Ammirati, Enrico, Russo, Claudio, Montoli, Alberto, Mondino, Michele
Publikováno v:
In International Journal of Cardiology 15 July 2023 383:42-49