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On fake Brownian motions

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  • Oleszkiewicz, Krzysztof

Abstract

Recently Albin constructed an example of a continuous martingale different from the classical Brownian motion but with the same marginal distributions, thus improving on the result of Hamza and Klebaner. We present a simpler solution to this problem.

Suggested Citation

  • Oleszkiewicz, Krzysztof, 2008. "On fake Brownian motions," Statistics & Probability Letters, Elsevier, vol. 78(11), pages 1251-1254, August.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:11:p:1251-1254
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    Cited by:

    1. Mathias Beiglbock & Gudmund Pammer & Walter Schachermayer, 2021. "From Bachelier to Dupire via Optimal Transport," Papers 2106.12395, arXiv.org.
    2. Mathias Beiglböck & Gudmund Pammer & Walter Schachermayer, 2022. "From Bachelier to Dupire via optimal transport," Finance and Stochastics, Springer, vol. 26(1), pages 59-84, January.
    3. Grahovac, Danijel, 2020. "Multifractal processes: Definition, properties and new examples," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Mathias Beiglbock & George Lowther & Gudmund Pammer & Walter Schachermayer, 2021. "Faking Brownian motion with continuous Markov martingales," Papers 2109.12927, arXiv.org.
    5. Henry-Labordère, Pierre & Tan, Xiaolu & Touzi, Nizar, 2016. "An explicit martingale version of the one-dimensional Brenier’s Theorem with full marginals constraint," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2800-2834.

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