Extreme value statistics of jump processes - Laboratoire de Physique Théorique de la Matière Condensée
Article Dans Une Revue Physical Review E Année : 2024

Extreme value statistics of jump processes

Résumé

We investigate extreme value statistics (EVS) of general discrete time and continuous space symmetric jump processes. We first show that for unbounded jump processes, the semi-infinite propagator G0(x, n), defined as the probability for a particle issued from 0 to be at position x after n steps whilst staying positive, is the key ingredient needed to derive a variety of joint distributions of extremes and times at which they are reached. Along with exact expressions, we extract novel universal asymptotic behaviors of such quantities. For bounded, semi-infinite jump processes killed upon first crossing of zero, we introduce the strip probability µ0,x(n), defined as the probability that a particle issued from 0 remains positive and reaches its maximum x on its n th step exactly. We show that µ0,x(n) is the essential building block to address EVS of semi-infinite jump processes, and obtain exact expressions and universal asymptotic behaviors of various joint distributions.
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Dates et versions

hal-04774752 , version 1 (08-11-2024)

Identifiants

Citer

J. Klinger, R. Voituriez, O. Bénichou. Extreme value statistics of jump processes. Physical Review E , 2024, 109 (5), pp.L052101. ⟨10.1103/PhysRevE.109.L052101⟩. ⟨hal-04774752⟩
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