Abstract.
Any solution of the functional equation
where B is a Brownian motion, behaves like a reflected Brownian motion, except when it attains a new maximum: we call it an α-perturbed reflected Brownian motion. Similarly any solution of
behaves like a Brownian motion except when it attains a new maximum or minimum: we call it an α,β-doubly perturbed Brownian motion. We complete some recent investigations by showing that for all permissible values of the parameters α, α and β respectively, these equations have pathwise unique solutions, and these are adapted to the filtration of B.
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Received: 7 November 1997 / Revised version: 13 July 1998
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Chaumont, L., Doney, R. Pathwise uniqueness for perturbed versions of Brownian motion and reflected Brownian motion. Probab Theory Relat Fields 113, 519–534 (1999). https://doi.org/10.1007/s004400050216
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DOI: https://doi.org/10.1007/s004400050216
- Mathematics Subject Classification (1991): 60J30, 60J20