On Doob's maximal inequality for Brownian motion

S. E. Graversen and G. Peskir

Stochastic Processes and their Applications, 1997, vol. 69, issue 1, 111-125

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

Keywords: Doob's maximal inequality; Brownian motion Optimal stopping (time) The principle of smooth fit Submartingale The maximality principle Stephan's problem with moving boundary Ito-Tanaka's formula Burkholder-Gundy's inequality (search for similar items in EconPapers)
Date: 1997
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