Transition Functions of Diffusion Processes on the Thoma Simplex

@article{Korotkikh2020TransitionFO,
  title={Transition Functions of Diffusion Processes on the Thoma Simplex},
  author={Sergei Korotkikh},
  journal={Functional Analysis and Its Applications},
  year={2020},
  volume={54},
  pages={118-134}
}
  • S. Korotkikh
  • Published 19 June 2018
  • Mathematics
  • Functional Analysis and Its Applications
The paper deals with a three-dimensional family of diffusion processes on an infinite-dimensional simplex. These processes were constructed by Borodin and Olshanski in 2009 and 2010, and they include, as limit objects, the infinitely-many-neutral-allels diffusion model constructed by Ethier and Kurtz in 1981 and its extension found by Petrov in 2009. Each process X in our family possesses a unique symmetrizing measure M, called the z-measure. Our main result is that the transition function of X… 

The Topological Support of the z-Measures on the Thoma Simplex

  • G. Olshanski
  • Mathematics
    Functional Analysis and Its Applications
  • 2018
The Thoma simplex Ω is an infinite-dimensional space, a kind of dual object to the infinite symmetric group. The z-measures are probability measures on Ω depending on three continuous parameters. One

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The Topological Support of the z-Measures on the Thoma Simplex

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