2011/02/19 by Raluca M. Balan, Raluca Balan, Balan, Raluca · 2 citations
Economics, Econometrics and Finance · Mathematics · #60G51 #60H05 #60H15 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60G51 #msc:60H05 #msc:60H15
paper · pdf · doi:10.48550/arxiv.1102.3992
37 pages
arxiv created 2011/02/19 · openalex publication_date 2011/02/19 · arxiv updated 2011/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we identify the necessary and sufficient conditions for the existence of a random field solution for some linear s.p.d.e.'s of parabolic and hyperbolic type. These equations rely on a spatial operator \cL given by the L2-generator of a d-dimensional Lévy process X=(Xt)t ≥ 0, and are driven by a spatially-homogeneous Gaussian noise, which is fractional in time with Hurst index H>1/2. As an application, we consider the case when X is a β-stable process, with β∈ (0,2]. In the parabolic case, we develop a connection with the potential theory of the Markov process X (defined as the symmetrization of X), and we show that the existence of the solution is related to the existence of a "weighted" intersection local time of two independent copies of X.