Nonergodicity of reset geometric Brownian motion
Deepak Vinod, Andrey G. Cherstvy, Wei Wang, Ralf Metzler, Igor M. Sokolov
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.
Topics & Concepts
ErgodicityReset (finance)Brownian motionStatistical physicsPoisson distributionPhysicsBrownian motorClassical mechanicsMathematicsQuantum mechanicsStatisticsWork (physics)RatchetFinancial economicsEconomicsDiffusion and Search DynamicsEvolution and Genetic Dynamics