arXiv subjects

Kiyotaka Suzaki

Publications and source records attributed to Kiyotaka Suzaki.

2 recordsLinked to original sources

arXiv2021

A limit theorem for persistence diagrams of random filtered complexes built over marked point processes

We consider random filtered complexes built over marked point processes on Euclidean spaces. Examples of our filtered complexes include a filtration of $\check{\textrm{C}}$ech complexes of a family of sets with various sizes, growths, and shapes. We establish the law of large numbers for persistence diagrams as the size of the convex window observing a marked point process tends to infinity.

math.PR↗

arXiv2020

Stochastic flows and rough differential equations on foliated spaces

Stochastic differential equations (SDEs) on compact foliated spaces were introduced a few years ago. As a corollary, a leafwise Brownian motion on a compact foliated space was obtained as a solution to an SDE. In this paper we construct stochastic flows associated with the SDEs by using rough path theory, which is something like a "deterministic version" of Itô's SDE theory.

math.DS↗