### Abstract

Let w (x, t) := (u, v)(x, t), x ∈ ℝ^{3}, t > 0, be the ℝ^{2}-valued spatial-temporal random field w = (u, v) arising from a certain two-equation system of time-fractional linear partial differential equations of reaction-diffusion-wave type, with given random initial data u(x,0), u_{t}(x,0), and v(x,0), v_{t}(x,0). We discuss the scaling limit, under proper homogenization and renormalization, of w(x,t), subject to suitable assumptions on the random initial conditions. Since the component fields u,v depend on the interactions present within the system, we employ a certain stochastic decoupling method to tackle this component dependence. The work shows, in particular, the various non-Gaussian scenarios proposed in [4, 13, 17] and the references therein, for the single diffusion type equations, in classical or in fractional time/space derivatives, can be studied for the two-equation system, in a significant way.

Original language | English |
---|---|

Pages (from-to) | 1-35 |

Number of pages | 35 |

Journal | Stochastics and Dynamics |

Volume | 10 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2010 Mar 1 |

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### All Science Journal Classification (ASJC) codes

- Modelling and Simulation

### Cite this

*Stochastics and Dynamics*,

*10*(1), 1-35. https://doi.org/10.1142/S0219493710002826

}

*Stochastics and Dynamics*, vol. 10, no. 1, pp. 1-35. https://doi.org/10.1142/S0219493710002826

**Scaling limits for time-fractional diffusion-wave systems with random initial data.** / Liu, Gi-Ren; Shieh, Narn Rueih.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Scaling limits for time-fractional diffusion-wave systems with random initial data

AU - Liu, Gi-Ren

AU - Shieh, Narn Rueih

PY - 2010/3/1

Y1 - 2010/3/1

N2 - Let w (x, t) := (u, v)(x, t), x ∈ ℝ3, t > 0, be the ℝ2-valued spatial-temporal random field w = (u, v) arising from a certain two-equation system of time-fractional linear partial differential equations of reaction-diffusion-wave type, with given random initial data u(x,0), ut(x,0), and v(x,0), vt(x,0). We discuss the scaling limit, under proper homogenization and renormalization, of w(x,t), subject to suitable assumptions on the random initial conditions. Since the component fields u,v depend on the interactions present within the system, we employ a certain stochastic decoupling method to tackle this component dependence. The work shows, in particular, the various non-Gaussian scenarios proposed in [4, 13, 17] and the references therein, for the single diffusion type equations, in classical or in fractional time/space derivatives, can be studied for the two-equation system, in a significant way.

AB - Let w (x, t) := (u, v)(x, t), x ∈ ℝ3, t > 0, be the ℝ2-valued spatial-temporal random field w = (u, v) arising from a certain two-equation system of time-fractional linear partial differential equations of reaction-diffusion-wave type, with given random initial data u(x,0), ut(x,0), and v(x,0), vt(x,0). We discuss the scaling limit, under proper homogenization and renormalization, of w(x,t), subject to suitable assumptions on the random initial conditions. Since the component fields u,v depend on the interactions present within the system, we employ a certain stochastic decoupling method to tackle this component dependence. The work shows, in particular, the various non-Gaussian scenarios proposed in [4, 13, 17] and the references therein, for the single diffusion type equations, in classical or in fractional time/space derivatives, can be studied for the two-equation system, in a significant way.

UR - http://www.scopus.com/inward/record.url?scp=77951166931&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951166931&partnerID=8YFLogxK

U2 - 10.1142/S0219493710002826

DO - 10.1142/S0219493710002826

M3 - Article

VL - 10

SP - 1

EP - 35

JO - Stochastics and Dynamics

JF - Stochastics and Dynamics

SN - 0219-4937

IS - 1

ER -