Zobrazeno 1 - 10
of 186
pro vyhledávání: '"Bălan, Raluca"'
Autor:
Balan, Raluca M., Jiménez, Juan J.
In this article, we examine a stochastic partial differential equation (SPDE) driven by a symmetric $\alpha$-stable (S$\alpha$S) L\'evy noise, that is multiplied by a linear function $\sigma(u)=u$ of the solution. The solution is interpreted in the m
Externí odkaz:
http://arxiv.org/abs/2409.12286
In this paper, we present an almost sure central limit theorem (ASCLT) for the hyperbolic Anderson model (HAM) with a L\'evy white noise in a finite-variance setting, complementing a recent work by Balan and Zheng (\emph{Trans.~Amer.~Math.~Soc.}, 202
Externí odkaz:
http://arxiv.org/abs/2310.10784
In this article, we consider the stochastic wave equation in spatial dimension $d=1$, with linear term $\sigma(u)=u$ multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with Hurst index $H
Externí odkaz:
http://arxiv.org/abs/2307.00103
Autor:
Balan, Raluca M., Liang, Xiao
In this article, we study the continuity in law of the solutions of two linear multiplicative SPDEs (the parabolic Anderson model and the hyperbolic Anderson model) with respect to the spatial parameter of the noise. The solution is interpreted in th
Externí odkaz:
http://arxiv.org/abs/2305.10330
Autor:
Balan, Raluca M., Yuan, Wangjun
In this article, we study the hyperbolic Anderson model in dimension 1, driven by a time-independent rough noise, i.e. the noise associated with the fractional Brownian motion of Hurst index $H \in (1/4,1/2)$. We prove that, with appropriate normaliz
Externí odkaz:
http://arxiv.org/abs/2305.05043
Autor:
Balan, Raluca M., Zheng, Guangqu
Publikováno v:
Trans. Amer. Math. Soc. (2024)
In this paper, we study one-dimensional hyperbolic Anderson models (HAM) driven by space-time pure-jump L\'evy white noise in a finite-variance setting. Motivated by recent active research on limit theorems for stochastic partial differential equatio
Externí odkaz:
http://arxiv.org/abs/2302.14178
In this note, we consider the parabolic Anderson model on $\mathbb{R}_{+} \times \mathbb{R}$, driven by a Gaussian noise which is fractional in time with index $H_0>1/2$ and fractional in space with index $03/4$. Under a gene
Externí odkaz:
http://arxiv.org/abs/2206.11361
Autor:
Balan, Raluca M., Yuan, Wangjun
In this article, we investigate the asymptotic behaviour of the spatial integral of the solution to the parabolic Anderson model with time independent noise in dimension $d\geq 1$, as the domain of the integral becomes large. We consider 3 cases: (a)
Externí odkaz:
http://arxiv.org/abs/2205.13105
Autor:
Balan, Raluca M., Yuan, Wangjun
In this article, we study the asymptotic behavior of the spatial integral of the solution to the hyperbolic Anderson model in dimension $d\leq 2$, as the domain of the integral gets large (for fixed time $t$). This equation is driven by a spatially h
Externí odkaz:
http://arxiv.org/abs/2201.02319
Autor:
Balan, Raluca M.
Publikováno v:
ALEA, Latin American Journal of Probability and Mathematical Statistics 20 (2023), 463-496
In this article, we study the stochastic wave equation on the entire space $\mathbb{R}^d$, driven by a space-time L\'evy white noise with possibly infinite variance (such as the $\alpha$-stable L\'evy noise). In this equation, the noise is multiplied
Externí odkaz:
http://arxiv.org/abs/2111.14242