Geodesic
An example of a~stochastic differential equation which has no strong solution
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 427-430

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An example of a stochastic differential equation $dx_t=A(t,x)\,dt+dw_t$ with $|A(t,x)|\le1$ is given which has no solution $\{x_t\}$ well adapted to $\{w_t\colon s\in[0,t]\}$. 
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     author = {B. S. Tsirel'son},
     title = {An example of a~stochastic differential equation which has no strong solution},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     publisher = {mathdoc},
     volume = {20},
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     year = {1975},
     language = {ru},
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B. S. Tsirel'son. An example of a~stochastic differential equation which has no strong solution. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 427-430. http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a19/