Using additive functionals to embed preassigned distributions in symmetric stable processes

Monroe, Itrel

doi:10.1090/S0002-9947-1972-0298768-8

Using additive functionals to embed preassigned distributions in symmetric stable processes
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by Itrel Monroe

Trans. Amer. Math. Soc. 163 (1972), 131-146

DOI: https://doi.org/10.1090/S0002-9947-1972-0298768-8

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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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Construction of almost surely convergent random processes

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