"My drift" has appeared in the work

B.S. Tsirelson, "An example of a stochastic differential equation having no strong solution." Theory Probab. Appl. 20:2, 416-418 (1975) (transl. from Russian). [MR51#11654]

See also:

M. Yor, "Tsirel'son's equation in discrete time." Probab. Theory Relat. Fields 91:2, 135-152 (1992). [MR93d:60104]

L.C.G. Rogers, D. Williams, "Diffusions, Markov processes, and martingales. Vol. 2: Itô calculus." John Wiley & sons, 1987. [MR89k:60117]

Tsirel'son's example. This is a celebrated and mysterious example of a '1-dimensional' equation of type:

dX = dB + b(t,X.) dt, X(0)=0,

where b is a uniformly bounded previsible path functional. This equation automatically has a weak solution unique in law. For Tsirel'son's inspired choice of the functional b, X cannot be measurable on the filtration of B. This is an important counterexample in connection with the innovations problem in the theory of filtering.
(Rogers and Williams, V.3.18 on p. 155.)

Citing works, 1975-2005

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  1975      1980                1990                2000

Attal, Benes, Buckdahn, Burdzy, Cherny, Chitashvili, Cutland, Dorogovtsev, Émery, Engelbert, Feldman, Fleming, Gyongy, Hu, Kallianpur, Kallsen, Krylov, Le Gall, Mel'nikov, Mosca, Pardoux, Pisanets, Rascani, Revuz, Rogers, Schachermayer, Smorodinsky, Stroock, Toronjadze, Uchida, Vershik, Watanabe, Weizsäcker, Williams, Yor. (Detail)