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Short Communications

An example of a stochastic differential equation which has no strong solution

B. S. Tsirel'son

Leningrad

Abstract: 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 $\{w_t\colon s\in[0,t]\}$.

Received: 16.12.1974

 English version: Theory of Probability and its Applications, 1976, 20:2, 416–418

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