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Survival probability of stochastic processes beyond persistence exponents.

Abstract：

:For many stochastic processes, the probability [Formula: see text] of not-having reached a target in unbounded space up to time [Formula: see text] follows a slow algebraic decay at long times, [Formula: see text]. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent [Formula: see text] has been studied at length, the prefactor [Formula: see text], which is quantitatively essential, remains poorly characterized, especially for non-Markovian processes. Here we derive explicit expressions for [Formula: see text] for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for [Formula: see text] are in good agreement with numerical simulations, even for strongly correlated processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.

journal_name

Nat Commun

journal_title

Nature communications

authors

Levernier N,Dolgushev M,Bénichou O,Voituriez R,Guérin T

doi

10.1038/s41467-019-10841-6

subject

Has Abstract

pub_date

2019-07-05 00:00:00

pages

2990

issue

1

issn

2041-1723

pii

10.1038/s41467-019-10841-6

journal_volume

10

pub_type

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