3 papers
math.PR2026
Brownian motion: the hyperbolic number setting
Daniel Alpay, Ilwoo Cho, Liora Mayats-Alpay
The purpose of this paper is to define normal Gaussian variables in the setting of hyperbolic probabilities, and introduce an associated Brownian motion, when both the index and th…
math.FA2025
The Kaczmarz Algorithm in Hilbert -modules
Daniel Alpay, Chad Berner, Eric S. Weber
The Kaczmarz algorithm in Hilbert spaces is a classical iterative method for stably recovering vectors from inner product data. In this paper, we extend the algorithm to the settin…
math.PR2025
Analytic continuation of time in Brownian motion. Stochastic distributions approach
Luis Daniel Abreu, Daniel Alpay, Tryphon Georgiou +1
With the use of Hida's white noise space theory space theory and spaces of stochastic distributions, we present a detailed analytic continuation theory for classes of Gaussian proc…