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The coalescent in population models with time-inhomogeneous environment. (English) Zbl 1064.92034
Summary: The coalescent theory, well developed for the class of exchangeable population models with time-homogeneous reproduction law, is extended to a class of population models with time-inhomogeneous environment, where the population size is allowed to vary deterministically with time and where the distribution of the family sizes is allowed to change from generation to generation. A new class of time-inhomogeneous coalescent limit processes with simultaneous multiple mergers arises. Its distribution can be characterized in terms of product integrals.

92D15Problems related to evolution
60J70Applications of Brownian motions and diffusion theory
60F17Functional limit theorems; invariance principles
Full Text: DOI
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