First Passage Under Restart

TL;DR

This paper develops a universal framework for analyzing first passage processes under restart mechanisms, revealing fundamental principles that apply broadly, especially exemplified by diffusion processes.

Contribution

It introduces a generic approach to first passage under restart, demonstrating the universality of diffusion under restart and enabling broader understanding of complex stochastic processes.

Findings

Universal behavior of diffusion under restart

A generic method for first passage under restart

Extension of universality to complex processes

Abstract

First passage under restart has recently emerged as a conceptual framework suitable for the description of a wide range of phenomena, but the endless variety of ways in which restart mechanisms and first passage processes mix and match hindered the identification of unifying principles and general truths. Hope that these exist came from a recently discovered universality displayed by processes under optimal, constant rate, restart---but extensions and generalizations proved challenging as they marry arbitrarily complex processes and restart mechanisms. To address this challenge, we develop a generic approach to first passage under restart. Key features of diffusion under restart---the ultimate poster boy for this wide and diverse class of problems---are then shown to be completely universal.