Archive ouverte HAL – Properties of additive functionals of Brownian motion with resetting

Frank Den Hollander 1 Satya N. Majumdar 2 Janusz M. Meylahn 1 Hugo Touchette 3

Frank Den Hollander, Satya N. Majumdar, Janusz M. Meylahn, Hugo Touchette. Properties of additive functionals of Brownian motion with resetting. Journal of Physics A: Mathematical and General , IOP Publishing, 2019. ⟨hal-02102127⟩

We study the distribution of additive functionals of reset Brownian motion, a variation of normal Brownian motion in which the path is interrupted at a given rate and placed back to a given reset position. Our goal is two-fold: (1) For general functionals, we derive a large deviation principle in the presence of resetting and identify the large deviation rate function in terms of a variational formula involving large deviation rate functions without resetting. (2) For three examples of functionals (positive occupation time, area and absolute area), we investigate the effect of resetting by computing distributions and moments, using a formula that links the generating function with resetting to the generating function without resetting.

  • 1. Leiden University
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 3. Institute of Theoretical Physics