分野別セミナー

The Bernstein operator is a positive linear operator on the Banach
space of continuous functions on $[0,1]$,
which is used to show the celebrated Weierstrass approximation theorem
from a probabilistic perspective.
In this talk, we introduce an extension of the Bernstein operator to the
multidimensional cases
and discuss some limit theorems for the iterates of the operator.
As the limit, we capture the multidimensional Wright--Fisher diffusion
with mutation which is well-studied in population genetics.
Some further possible directions of these limit theorems including
infinite-dimensional cases are discussed as well.
Based on a joint work with Takatoshi Hirano.