Population processes sampled at random times

TL;DR

This paper analyzes various population processes sampled at random times, focusing on their first-passage times, hitting probabilities, and long-term behavior, with applications in ecology, epidemics, and finance.

Contribution

It introduces a comprehensive study of birth and death processes at Poisson times, including their hitting times and long-range behavior, expanding modeling capabilities for complex systems.

Findings

Derived distributions for first-passage times.

Analyzed long-range behavior of population jumps.

Applicable models for ecology, epidemics, and finance.

Abstract

In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are investigated. In particular, we study the hitting times in all cases and examine their long-range behavior. The time-changed population models considered here display upward (Birth process) and downward jumps (death processes) of arbitrary size and, for this reason, can be adopted as adequate models in ecology, epidemics and finance situations, under stress conditions.