Ergodic inequality of a two-parameter infinitely-many-alleles diffusion model. (English) Zbl 1322.60166

Zhou, Youzhou

J. Appl. Probab. 52, No. 1, 238-246 (2015).

Summary: In this paper, three models are considered. They are the infinitely-many-neutral-alleles model of S. N. Ethier and T. G. Kurtz [Adv. Appl. Probab. 13, 429–452 (1981; Zbl 0483.60076)], the two-parameter infinitely-many-alleles diffusion model of L. A. Petrov [Funct. Anal. Appl. 43, No. 4, 279–296 (2009); translation from Funkts. Anal. Prilozh. 43, No. 4, 45–66 (2009; Zbl 1204.60076)], and the infinitely-many-alleles model with symmetric dominance [S. N. Ethier and T. G. Kurtz, Ann. Probab. 26, No. 2, 533–561 (1998; Zbl 0940.60045)]. New representations of the transition densities are obtained for the first two models and the ergodic inequalities are provided for all three models.

MSC:

60J60	Diffusion processes
37A30	Ergodic theorems, spectral theory, Markov operators

Keywords:

infinitely-many-alleles diffusion model; Poisson-Dirichlet distribution; transition density; ergodic inequality

Citations:

Zbl 0483.60076; Zbl 1204.60076; Zbl 0940.60045