## B. Tsirelson | ## "My drift" | ## ideas noted |

"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

bis a uniformly bounded previsible path functional. This equation automatically has a weak solution unique in law. For Tsirel'son's inspired choice of the functionalb,Xcannot be measurable on the filtration ofB. 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.)

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 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)

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