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Some properties of superprocesses under a stochastic flow

Kijung Lee, Carl Mueller, Jie Xiong (2009)

Annales de l'I.H.P. Probabilités et statistiques

For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov’s Lp-theory for linear SPDE.

Some Theoretical Results on the Progeny of a Bisexual Galton-Watson Branching Process

González, M., Molina, M. (1997)

Serdica Mathematical Journal

A Superadditive Bisexual Galton-Watson Branching Process is considered and the total number of mating units, females and males, until the n-th generation, are studied. In particular some results about the stochastic monotony, probability generating functions and moments are obtained. Finally, the limit behaviour of those variables suitably normed is investigated.

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