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A discrete analogue and elementary derivation of 'Lévy's equivalence' for Brownian motion

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  • Simons, Gordon

Abstract

The present note presents a discrete analogue of Lévy's extended equivalence for symmetric simple random walks and provides an elementary derivation of Lévy's basic and extended based upon this analogue. Finally, it describes an almost sure version of the extended equivalence depending on an Ito-type stochastic integral.

Suggested Citation

  • Simons, Gordon, 1983. "A discrete analogue and elementary derivation of 'Lévy's equivalence' for Brownian motion," Statistics & Probability Letters, Elsevier, vol. 1(4), pages 203-206, June.
    • Handle: RePEc:eee:stapro:v:1:y:1983:i:4:p:203-206
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    Cited by:

    1. Fujita, Takahiko & Yagishita, Shotaro & Yoshida, Naohiro, 2024. "Some martingale properties of the simple random walk and its maximum process," Statistics & Probability Letters, Elsevier, vol. 208(C).

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    Keywords

    Wiener process Lévy's equivalence;

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