On the existence of universal functional solutions to classical SDE's
Kallenberg, Olav
Ann. Probab., Tome 24 (1996) no. 2, p. 196-205 / Harvested from Project Euclid
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Assume that the weak existence and pathwise uniqueness hold for solutions to the equation $dX_t=\sigma(t,X)dB_t + b(t,X)dt$ starting at fixed points. then there exists a Borel measurable function F, such that any solution (X,B) satisfies $X = F(X_0,B)$ a.s. This strengthens a fundamental result of Yamada and Watanbe, where F may depend on the initial distribution $\mu$
Publié le : 1996-01-14
Classification:  Weak and strong solutions,  pathwise uniqueness,  local martingale problem,  60H10,  60G44 
@article{1042644713,
     author = {Kallenberg, Olav},
     title = {On the existence of universal functional solutions to classical
			 SDE's},
     journal = {Ann. Probab.},
     volume = {24},
     number = {2},
     year = {1996},
     pages = { 196-205},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1042644713}
}

Kallenberg, Olav. On the existence of universal functional solutions to classical
			 SDE's. Ann. Probab., Tome 24 (1996) no. 2, pp.  196-205. http://gdmltest.u-ga.fr/item/1042644713/