The Distribution of Random Evolution in Erlang Semi-Marov Media
A. Pogorui
TL;DR
This paper investigates a one-dimensional random motion with Erlang-distributed sojourn times, deriving solutions to a fourth-order hyperbolic PDE specifically for the 2-Erlang case, advancing understanding of such stochastic processes.
Contribution
It introduces a novel analytical solution for the hyperbolic PDE governing Erlang semi-Markov media in the 2-Erlang case, expanding the mathematical framework of random motion models.
Findings
Derived explicit solutions for the 2-Erlang case
Extended the PDE framework for Erlang distributions
Enhanced modeling of semi-Markov media
Abstract
In this paper we study a one-dimensional random motion by having a general Erlang distribution for the sojourn times of the switching process and we obtain solution of the four order hyperbolic PDE for 2-Erlang case.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Mathematical Dynamics and Fractals · Stochastic processes and financial applications