Scaling limits for some PDE systems with random initial conditions
Resource
Stochastic Analysis and Applications, 28(3), 505-522
Journal
Stochastic Analysis and Applications
Pages
505-522
Date Issued
2010
Date
2010
Author(s)
Liu, Gi-Ren
Shieh, Narn-Rueih
Abstract
Let X = {X(x, t), x ∊ R n , t ∊ R +} be the R 2-valued spatial-temporal random field X = (u, v) arising from a certain two-equation system of parabolic linear partial differential equations with a given random initial condition X 0 = (u 0, v 0). We discuss the scaling limit of X under suitable conditions on X 0. Since the component fields u, v are dependent, even when the initial data u 0, v 0 are independent, the scaling limit is not readily reduced to the known single equation case. The correlated structure of random vector (u(x, t), v(x′, t′)) and the Hermite expansion associated with (u 0, v 0) play the essential roles in our study. The work shows, in particular, the non-Gaussian scenario proposed by Anh and Leonenko [2 Anh , V.V. , and Leonenko , N.N. 1999 . Non-Gaussian scenarios for the heat equation with singular initial data . Stochastic Process. Appl. 84 : 91 – 114 .[Crossref], [Web of Science ®] , [Google Scholar]] for the single heat equation can be discussed for the two-equation system, in a significant way.
Type
journal article
File(s)![Thumbnail Image]()
Loading...
Name
137.pdf
Size
23.81 KB
Format
Adobe PDF
Checksum
(MD5):1e2b69e03821d4a1e4cee1714acc64cd