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- Title
Continuity in law for solutions of SPDES with space-time homogeneous Gaussian noise.
- Authors
Balan, Raluca M.; Liang, Xiao
- Abstract
In this paper, 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 the Skorohod sense, using Malliavin calculus. We consider two cases: (i) the regular noise, whose spatial covariance is given by the Riesz kernel of order α ∈ (0 , d) , in spatial dimension d ≥ 1 ; (ii) the rough noise, which is fractional in space with Hurst index H < 1 / 2 , in spatial dimension d = 1. We assume that the noise is colored in time.
- Subjects
RANDOM noise theory; ANDERSON model; SPACETIME; STOCHASTIC partial differential equations; MALLIAVIN calculus; RIESZ spaces
- Publication
Stochastics & Dynamics, 2023, Vol 23, Issue 6, p1
- ISSN
0219-4937
- Publication type
Article
- DOI
10.1142/S0219493723500508