Vinod Deepak, Cherstvy Andrey G, Wang Wei, Metzler Ralf, Sokolov Igor M
Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.
Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin, Germany.
Phys Rev E. 2022 Jan;105(1):L012106. doi: 10.1103/PhysRevE.105.L012106.
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.
我们推导了泊松重置几何布朗运动（GBM）的系综平均和时间平均均方位移（MSD，TAMSD），结果与模拟一致。我们发现频繁重置时MSD和TAMSD会饱和，通过遍历性破坏参数量化TAMSD的离散程度，并计算价格分布。一般的MSD - TAMSD不等价证明了重置GBM是非遍历的。
