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Ergodicity breaking in geometric Brownian motion (1209.4517v3)
Published 20 Sep 2012 in math-ph, math.MP, and q-fin.RM
Abstract: Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time-average. A common tactic for bringing time averages closer to ensemble averages is diversification. In this letter we study the effects of diversification using the concept of ergodicity breaking.