5 papers
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…
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…
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…
Dynamics of Periodic Bubbles and Crashes: Modeling Market Overheating and Panic Selling via Cubic Momentum
Naohiro Yoshida
This paper proposes a simple and parsimonious discrete-time simulation model to describe the endogenous formation and periodic collapse of financial bubbles. While existing literat…
Some Martingale Properties of Simple Random Walk and Its Maximum Process
Takahiko Fujita, Shotaro Yagishita, Naohiro Yoshida
In this paper, martingales related to simple random walks and their maximum process are investigated. First, a sufficient condition under which a function with three arguments, tim…