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Published in:
2015 | OriginalPaper | Chapter
6. Processes of Wright-Fisher Type
Author : Aurélien Alfonsi
Published in: Affine Diffusions and Related Processes: Simulation, Theory and Applications
Publisher: Springer International Publishing
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Abstract
The main focus of this book is on affine diffusions and their simulation. In this chapter, we go slightly beyond this scope in the sense that the processes that we consider are not affine. They however have a clear connection with affine processes and belong to the class of Polynomial processes introduced by Cuchiero et al. [34] that also includes Affine diffusions. We first present Wright-Fisher processes that are well known in biology to model the frequency of a gene. These processes are directly related to Cox-Ingersoll-Ross diffusions, and we explain how it is possible to get second order schemes for these processes by reusing the second order schemes that we have developed for the CIR diffusion.