Martingale Functions of Brownian Motion and its Local Time

Martingale Functions of Brownian Motion and its Local Time


P.J. Fitzsimmons and D.M. Wroblewski




We characterize the class of local martingales of the form H(Bt , Lt) for a standard one-dimensional Brownian motion B=(Bt)t >= 0 and its local time at 0, L=(Lt)t >= 0. The main result is closely related to work of J. Oblój, who studied the local martingales of the form H(Bt , St), where St = sup0 <= s <= t Bs.

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July 12, 2007