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.

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Keywords limit theorems, multiple Wiener integrals, Random evolution, renormalization
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Journal Journal of Multivariate Analysis
Dawson, D.A, & Salehi, H. (Habib). (1980). Spatially homogeneous random evolutions. Journal of Multivariate Analysis, 10(2), 141–180. doi:10.1016/0047-259X(80)90012-3