7 papers
Chaotic CLT using Poisson Fourth Moment Theorem and Graph Theory
Raluca M. Balan, Jaime Garza
In this article, we consider the parabolic Anderson model and the hyperbolic Anderson model in dimension 1, driven by a time-independent Lévy noise, which is either white, or color…
A functional central limit theorem for the KPZ equation with narrow wedge initial data
Raluca M. Balan, Le Chen, Jinxin Wang
In this article, we consider the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge initial data. We prove a functional central limit theorem for the spatial average of the solut…
Gaussian fluctuations for the parabolic Anderson model with Lévy white noise
Raluca M. Balan, Matis Le Gall, Jinxin Wang
In this article, we consider the parabolic Anderson model driven by a Lévy white noise with finite variance in dimension 1, and we study the asymptotic behaviour of the spatial ave…
Itô integral for a two-sided Lévy process
Raluca M. Balan, Jaime Garza
In this article, we construct an Itô integral with respect to a two-sided finite-variance Lévy process , without a Gaussian component. Using Rosenthal i…
SPDEs with time-independent Lévy colored noise
Raluca M. Balan, Jinxin Wang
In this article, we introduce a time-independent version of the Lévy colored noise considered in Balan (2015) and Balan and Jiménez (2026). We study the existence of the solution o…
Gaussian fluctuations for the nonlinear stochastic heat equation with drift
Raluca M. Balan, Michael Salins
In this article, we prove the Quantitative Central Limit Theorem (QCLT) for the spatial average of the solution of the nonlinear stochastic heat equation with constant initial cond…
Integration with respect to Lévy colored noise, with applications to SPDEs
Raluca Balan
In this article, we introduce a Lévy analogue of the spatially homogeneous Gaussian noise of Dalang (1999), and we construct a stochastic integral with respect to this noise. The s…