Korean J. Math. Vol. 27 No. 1 (2019) pp.1-8
DOI: https://doi.org/10.11568/kjm.2019.27.1.1

On the representation of probability vector with special diffusion operator using the mutation and gene conversion rate

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Published: Mar 30, 2019
Keywords:
martingale problem, mutation and gene conversion, diffusion operator
Mathematics Subject Classification:
92D10, 60H30, 60G44.

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Won Choi
Department of Mathematics, Incheon National University, Incheon, Republic of Korea

Abstract

We will deal with an $n$ locus model in which mutation and gene conversion are taken into consideration. Also random partitions of the number $n$ determined by chromosomes with $n$ loci should be investigated. The diffusion process describes the time evolution of distributions of the random partitions. In this paper, we find the probability of distribution of the diffusion process with special diffusion operator $L_1$ and we show that the average probability of genes at different loci on one chromosome can be described by the rate of gene frequency of mutation and gene conversion.


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Supporting Agencies

This research was supported by Incheon National University Research Grant 2018-2019.

References

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