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Ergodicity breaking in geometric Brownian motion


  • Ole Peters
  • William Klein


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.

Suggested Citation

  • Ole Peters & William Klein, 2012. "Ergodicity breaking in geometric Brownian motion," Papers 1209.4517,, revised Mar 2013.
  • Handle: RePEc:arx:papers:1209.4517

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    Cited by:

    1. Ole Peters & Murray Gell-Mann, 2014. "Evaluating gambles using dynamics," Papers 1405.0585,, revised Jun 2015.
    2. Máté, Gabriell & Néda, Zoltán, 2016. "The advantage of inhomogeneity — Lessons from a noise driven linearized dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 310-317.
    3. Ole Peters & Alexander Adamou, 2018. "The sum of log-normal variates in geometric Brownian motion," Papers 1802.02939,
    4. Ole Peters & Alexander Adamou, 2015. "An evolutionary advantage of cooperation," Papers 1506.03414,, revised May 2018.

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