# From Markovian to non-Markovian persistence exponents

Source: [From Markovian to non-Markovian persistence exponents](<https://www.sota2.com/research/paper/68fa318b1e209131ce87f7e3>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T03:34:51.830Z

Authors: Julien Randon-Furling

Published: 2014-12-23T15:02:32.000Z

## Abstract

We establish an exact formula relating the survival probability for certain L\\'evy flights (viz. asymmetric $\\alpha$-stable processes where $\\alpha = 1/2$) with the survival probability for the order statistics of the running maxima of two independent Brownian particles. This formula allows us to show that the persistence exponent $\\delta$ in the latter, non Markovian case is simply related to the persistence exponent $\\theta$ in the former, Markovian case via: $\\delta=\\theta/2$. Thus, our formula reveals a link between two recently explored families of anomalous exponents: one exhibiting continuous deviations from Sparre-Andersen universality in a Markovian context, and one describing the slow kinetics of the non Markovian process corresponding to the difference between two independent Brownian maxima.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1412.7393>)

[PDF](<https://arxiv.org/pdf/1412.7393.pdf>)