Nonergodicity of reset geometric Brownian motion

被引：41

作者：

Vinod, Deepak ^{[1
]}

Cherstvy, Andrey G. ^{[1
,2
]}

Wang, Wei ^{[3
]}

Metzler, Ralf ^{[1
]}

Sokolov, Igor M. ^{[2
,4
]}

机构：

[1] Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany

[2] Humboldt Univ, Inst Phys, D-12489 Berlin, Germany

[3] Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany

[4] IRIS Adlershof, D-12489 Berlin, Germany

来源：

PHYSICAL REVIEW E | 2022年 / 105卷 / 01期

关键词：

PATH-DEPENDENT OPTIONS; LOOKBACK;

D O I：

10.1103/PhysRevE.105.L012106

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

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.

引用

页数：4

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