Abstract
Following Skorokhod, several authors in recent years have proposed methods to define a stopping time $T$ for Brownian motion $({X_t},{\mathcal {F}_t})$ such that ${X_T}$ will have some preassigned distribution. In this paper a method utilizing additive functionals is explored. It is applicable not only to Brownian motion but all symmetric stable processes of index $\alpha > 1$. Using this method one is able to obtain any distribution having a finite $\alpha - 1$ absolute moment. There is also a discussion of the problem of approximating symmetric stable processes with random walks.
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More From: Transactions of the American Mathematical Society
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