Moran random walk with reset and short memory
We investigated the statistical properties of the Moran random walk (Y_n)_n in one dimension, focusing on short memory. Specifically, employing generating function techniques, we determined the cumulative distribution function and the mean of the height H_n. Furthermore, we derived explicit expressions for the distribution, mean, and variance of Y_n, along with its asymptotic distribution. Finally, we provided the distribution of the waiting time τ_h, which represents the number of steps required to reach a specified level h, as the conclusion of our study.
In this paper we present a general mathematical construction that allows us to define a parametric class of non-Gaussian processes, namely degenerate Brownian motion (dBm). This class, is made up…
The goal of this paper is to present new results on generalized polynomial sequence known as degenerate Lévy-Meixner Appell polynomials associated with the infinite-dimensional degenerate Lévy-…