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math.PR2026
An alternative formulation of the discrete-time fractional Poisson process
Naohiro Yoshida
This paper introduces a discrete-time fractional Poisson process defined as a renewal process, where the waiting times follow a discrete Mittag-Leffler distribution. We investigate…
math.PR2026
Analysis of an Inhomogeneous Random Walk with Spatial Decay of Transition Probabilities and Parameter Renewal per Excursion
Naohiro Yoshida
In this paper, we propose and analyze a novel one-dimensional inhomogeneous random walk model that combines spatial decay of transition probabilities with a temporal renewal struct…
math.PR2026
Poisson Hyperbolic Staircase in Discrete Time
Naohiro Yoshida
In this paper, we propose a novel stochastic process that serves as a natural discrete-time counterpart to the continuous-time model known as the ``Poisson hyperbolic staircase'' p…