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Spatially homogeneous random evolutions

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  • Dawson, Donald A.
  • Salehi, Habib

Abstract

Spatially homogeneous random evolutions arise in the study of the growth of a population in a spatially homogeneous random environment. The random evolution is obtained as the solution of a bilinear stochastic evolution equation. The main results are concerned with the asymptotic behavior of the solution for large times. In particular, conditions for the existence of a stationary random field are established. Furthermore space-time renormalization limit theorems are obtained which lead to either Gaussian or non-Gaussian generalized processes depending on the case under consideration.

Suggested Citation

  • Dawson, Donald A. & Salehi, Habib, 1980. "Spatially homogeneous random evolutions," Journal of Multivariate Analysis, Elsevier, vol. 10(2), pages 141-180, June.
    • Handle: RePEc:eee:jmvana:v:10:y:1980:i:2:p:141-180
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    Cited by:

    1. Basson, Arnaud, 2008. "Spatially homogeneous solutions of 3D stochastic Navier-Stokes equations and local energy inequality," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 417-451, March.
    2. Talarczyk, Anna, 2001. "Self-intersection local time of order k for Gaussian processes in," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 17-72, November.
    3. Tessitore, Gianmario & Zabczyk, Jerzy, 1998. "Strict positivity for stochastic heat equations," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 83-98, September.
    4. T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2004. "Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Cases of Large and Critical Dimensions," RePAd Working Paper Series lrsp-TRS404, Département des sciences administratives, UQO.
    5. Bojdecki, T. & Gorostiza, L.G. & Talarczyk, A., 2006. "Limit theorems for occupation time fluctuations of branching systems II: Critical and large dimensions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 19-35, January.
    6. Choi, Jae-Hwan & Han, Beom-Seok, 2021. "A regularity theory for stochastic partial differential equations with a super-linear diffusion coefficient and a spatially homogeneous colored noise," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 1-30.
    7. Bojdecki, Tomasz & Jakubowski, Jacek, 1999. "Invariant measures for generalized Langevin equations in conuclear space," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 1-24, November.

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