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  • Letter

Nonergodicity of reset geometric Brownian motion

Deepak Vinod1,*, Andrey G. Cherstvy2,1,†, Wei Wang3,‡, Ralf Metzler1,§, and Igor M. Sokolov2,4,∥

  • 1Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
  • 2Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin, Germany
  • 3Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
  • 4IRIS Adlershof, 12489 Berlin, Germany

  • *ugdeepakv@gmail.com
  • †a.cherstvy@gmail.com
  • ‡weiwangnuaa@gmail.com
  • §rmetzler@uni-potsdam.de
  • ∥igor.sokolov@physik.hu-berlin.de
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Phys. Rev. E 105, L012106 – Published 31 January, 2022

DOI: https://doi.org/10.1103/PhysRevE.105.L012106

Abstract

We derive. the ensemble- and time-averaged mean-squared displacements (MSD, TAMSD) for Poisson-reset geometric Brownian motion (GBM), in agreement with simulations. We find MSD and TAMSD saturation for frequent resetting, quantify the spread of TAMSDs via the ergodicity-breaking parameter and compute distributions of prices. General MSD-TAMSD nonequivalence proves reset GBM nonergodic.

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Phys. Rev. E 105, L012106– Published 31 January, 2022
  • Received 12 October 2021
  • Accepted 10 January 2022
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