Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise

2018/05/17 by Raluca M. Balan, Balan, Raluca M., Lluís Quer-Sardanyons +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1805.06936

openalex publication_date 2018/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we consider the stochastic wave equation on ℝ₊ × ℝ, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structures are given by locally integrable functions γ (in time) and f (in space), which are the Fourier transforms of tempered measures ν on ℝ, respectively μ on ℝ. Our main result shows that the law of the solution u(t,x) of this equation is absolutely continuous with respect to the Lebesgue measure.

Citations

• Asymptotics of the density of parabolic Anderson random fields
• A Central Limit Theorem for the stochastic heat equation

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