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On Doob's maximal inequality for Brownian motion

Author

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  • Graversen, S. E.
  • Peskir, G.

Abstract

If B = (Bt)t [greater-or-equal, slanted] 0 is a standard Brownian motion started at x under Px for x [greater-or-equal, slanted] 0, and [tau] is any stopping time for B with Ex([tau]) 1 the following inequality is shown to be sharp: The sharpness is realized through the stopping times of the form for which it is computed: whenever [var epsilon] > 0 and 0 0 and all 0

Suggested Citation

  • Graversen, S. E. & Peskir, G., 1997. "On Doob's maximal inequality for Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 69(1), pages 111-125, July.
    • Handle: RePEc:eee:spapps:v:69:y:1997:i:1:p:111-125
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    References listed on IDEAS

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    1. Jacka, S. D., 1988. "Doob's inequalities revisited: A maximal H1-embedding," Stochastic Processes and their Applications, Elsevier, vol. 29(2), pages 281-290, September.
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