4 papers · 1 filter
Quartic variation of the solution to the semilinear stochastic heat equation: limit behavior and asymptotic independence with respect to the data
I Cîmpean, Yassine Nachit, Ciprian A Tudor
This work concerns the limit behavior of the quartic variation (i.e., the power variation of order four) with respect to the time variable of the solution to the semilinear stochas…
Quantitative boundary Hölder estimates for the inhomogeneous Poisson problem through a probabilistic approach
Iulian Cîmpean, Ionel Popescu, Arghir Zarnescu
In this paper we derive quantitative boundary Hölder estimates, with explicit constants, for the inhomogeneous Poisson problem in a bounded open set . Our ap…
A probabilistic approach to spectral analysis of Cauchy-type inverse problems: Convergence and stability analysis
Iulian Cîmpean, Andreea Grecu, Liviu Marin
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse p…
Error analysis for the deep Kolmogorov method
Iulian Cîmpean, Thang Do, Lukas Gonon +2
The deep Kolmogorov method is a simple and popular deep learning based method for approximating solutions of partial differential equations (PDEs) of the Kolmogorov type. In this w…