Independence properties for tree beta models
co-authors: Makiko Sasada and Jacek Wesołowski.
preprint: arXiv:2609.15199 (2026)
We introduce two tree beta-type models and study their independence properties, complementing the Matsumoto–Yor and Hamza–Vallois tree models.
The Independence-Preserving Property and Planar Web Geometry
preprint: arXiv:2607.20646 (2026)
We use planar web geometry to study independence-preserving transformations and characterisations of probability laws. Abelian relations give a common framework for classical characterisation theorems and quadrirational Yang–Baxter maps.
Deep learning of point processes for modeling high-frequency data
co-authors: Ioane Muni Toke and Nakahiro Yoshida.
preprint: arXiv
We investigate applications of deep neural networks to a point process having an intensity with mixing covariates processes as input. Our generic model includes Cox-type models and marked point processes as well as multivariate point processes. An oracle inequality and a rate of convergence are derived for the prediction error. A simulation study shows that the marked point process can be superior to the simple multivariate model in prediction. We apply the marked ratio model to real limit order book data.