Scaling limits for some P.D.E. systems with random initial conditions

Gi-Ren Liu, Narn Rueih Shieh

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let X = {X(x, t), x ∈ ℝn, t ∈ R+} be the R2-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 X0 = (u0, v0). We discuss the scaling limit of X under suitable conditions on X0. Since the component fields u, v are dependent, even when the initial data u0, v0 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 (u0, v0) play the essential roles in our study. The work shows, in particular, the non-Gaussian scenario proposed by Anh and Leonenko [2] for the single heat equation can be discussed for the two-equation system, in a significant way.

Original languageEnglish
Pages (from-to)505-522
Number of pages18
JournalStochastic Analysis and Applications
Volume28
Issue number3
DOIs
Publication statusPublished - 2010 May 1

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Scaling Limit
Partial differential equations
Initial conditions
Hermite Expansion
Linear partial differential equation
Parabolic Partial Differential Equations
Random Vector
Heat Equation
Random Field
System of equations
Scenarios
Dependent
Hot Temperature
Scaling
Random field

All Science Journal Classification (ASJC) codes

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability

Cite this

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Scaling limits for some P.D.E. systems with random initial conditions. / Liu, Gi-Ren; Shieh, Narn Rueih.

In: Stochastic Analysis and Applications, Vol. 28, No. 3, 01.05.2010, p. 505-522.

Research output: Contribution to journalArticle

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