Ergodicity Breaking in Geometric Brownian Motion

The paper by Ole Peters and Bill Klein is published in Physical Review Letters. It takes issue with the common but false assumption of ergodicity — the equality of time averages and expectation values — for the most influential model in mathematical finance. While previous work has focused on either infinite-time averages for single systems, or averages over infinitely many systems in finite time, here the effects of ergodicity breaking are studied for finite averaging times and finite ensemble sizes. This makes the results more readily applicable to real physical systems.
O. Peters and W. Klein
Ergodicity Breaking in Geometric Brownian Motion
Phys. Rev. Lett. 110, 100603 (2013)
Open Access: arXiv:1209.4517

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