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June, 1979 Further Results on One-dimensional Diffusions with Time Parameter set S(- \infty, \infty)$
J. Theodore Cox
Ann. Probab. 7(3): 537-542 (June, 1979). DOI: 10.1214/aop/1176995054

Abstract

Let $p_t, t \geqslant 0$ be the probability transition semigroup of a continuous one-dimensional diffusion. We examine continuous Markov processes $\xi_s$, defined for $-\infty < s < \infty$, which are governed by $p_t$. It is shown that the class of such processes, modulo convex combinations and translations, can consist of at most three elements. In addition, it is shown that the first passage times for these processes are related to a previously known existence condition.

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J. Theodore Cox. "Further Results on One-dimensional Diffusions with Time Parameter set S(- \infty, \infty)$." Ann. Probab. 7 (3) 537 - 542, June, 1979. https://doi.org/10.1214/aop/1176995054

Information

Published: June, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0401.60073
MathSciNet: MR528331
Digital Object Identifier: 10.1214/aop/1176995054

Subjects:
Primary: 60J60
Secondary: 60J50

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 3 • June, 1979
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