# Bessel-like birth-death process

## TL;DR

This paper introduces a generalized Bessel-like birth-death process that bridges Markov chain models and SDEs, aiding in analyzing population and opinion dynamics with long-range memory effects.

## Contribution

The paper proposes a new Bessel-like birth-death process that provides a clear SDE representation, enhancing modeling flexibility and analytical capabilities.

## Key findings

- Derived equations for probability density functions of burst durations.
- Established the process's representation via SDEs.
- Facilitated analysis of long-range memory in population models.

## Abstract

We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the birth-death processes as the continuous-time Markov chains and the continuous SDEs is of high importance for the alternatives of modeling. We propose and generalize the Bessel-like birth-death process having clear representation by the SDEs. The new process helps to integrate the alternatives of description and to derive the equations for the probability density function (PDF) of the burst and inter-burst duration of the proposed continuous time birth-death processes.