Excursion Theory Revisited
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.
A hard copy of this manuscript is available from the
first-named author upon request.
The manuscript can also be downloaded in
dvi form (28K),
and pdf form (92K).
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July 12, 2007
