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Brownian motion Markovian stopping times with given laws

S. V. Anulova

Moscow

Abstract: Let $w_t$, $t\in[0,\infty)$, be the Brownian motion. For any probability law $\mu$ on $(0,\infty]$, there exists a subset $B$ of $[-\infty,\infty]\times(0,\infty]$ such that the distribution of the stopping time
$$ \tau=\inf\{t>0:(w_t,t)\in B\} $$
coincides with $\mu$.

Received: 28.09.1977

 English version: Theory of Probability and its Applications, 1981, 25:2, 362–366

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