Multi-scaling limits for relativistic diffusion equations with random initial data

Gi Ren Liu, Narn Rueih Shieh

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let u(t, x), t>0, x ∈ ℝn, be the spatial-temporal random field arising from the solution of a relativistic diffusion equation with the spatialfractional parameter α ∈ (0, 2) and the mass parameter m > 0, subject to a random initial condition u(0, x) which is characterized as a subordinated Gaussian field. In this article, we study the large-scale and the small-scale limits for the suitable space-time re-scalings of the solution field u(t, x). Both the Gaussian and the non-Gaussian limit theorems are discussed. The smallscale scaling involves not only scaling on u(t, x) but also re-scaling the initial data; this is a new type result for the literature. Moreover, in the two scalings the parameter α ∈ (0, 2) and the parameter m > 0 play distinct roles for the scaling and the limiting procedures.

Original languageEnglish
Pages (from-to)3423-3446
Number of pages24
JournalTransactions of the American Mathematical Society
Volume367
Issue number5
DOIs
Publication statusPublished - 2015 Jan 1

Fingerprint

Multiscaling
Scaling Limit
Diffusion equation
Scaling
Rescaling
Gaussian Fields
Limit Theorems
Random Field
Initial conditions
Limiting
Space-time
Distinct

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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title = "Multi-scaling limits for relativistic diffusion equations with random initial data",
abstract = "Let u(t, x), t>0, x ∈ ℝn, be the spatial-temporal random field arising from the solution of a relativistic diffusion equation with the spatialfractional parameter α ∈ (0, 2) and the mass parameter m > 0, subject to a random initial condition u(0, x) which is characterized as a subordinated Gaussian field. In this article, we study the large-scale and the small-scale limits for the suitable space-time re-scalings of the solution field u(t, x). Both the Gaussian and the non-Gaussian limit theorems are discussed. The smallscale scaling involves not only scaling on u(t, x) but also re-scaling the initial data; this is a new type result for the literature. Moreover, in the two scalings the parameter α ∈ (0, 2) and the parameter m > 0 play distinct roles for the scaling and the limiting procedures.",
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Multi-scaling limits for relativistic diffusion equations with random initial data. / Liu, Gi Ren; Shieh, Narn Rueih.

In: Transactions of the American Mathematical Society, Vol. 367, No. 5, 01.01.2015, p. 3423-3446.

Research output: Contribution to journalArticle

TY - JOUR

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