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Repeat distributions from unequal crossovers

Michael Baake (2008)

Banach Center Publications

It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with single crossovers is analysed that result in equilibrium distributions of this type. Due to the nonlinear and infinite-dimensional nature of these models, their analysis requires some nontrivial tools from measure theory and functional analysis, which makes them interesting...

Representation of Itô integrals by Lebesgue/Bochner integrals

Qi Lü, Jiongmin Yong, Xu Zhang (2012)

Journal of the European Mathematical Society

In [Yong 2004], it was proved that as long as the integrand has certain properties, the corresponding Itô integral can be written as a (parameterized) Lebesgue integral (or a Bochner integral). In this paper, we show that such a question can be answered in a more positive and refined way. To do this, we need to characterize the dual of the Banach space of some vector-valued stochastic processes having different integrability with respect to the time variable and the probability measure. The later...

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