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October, 1977 On One-Dimensional Diffusions with Time Parameter Set $(-\infty, \infty)$
J. Theodore Cox
Ann. Probab. 5(5): 807-813 (October, 1977). DOI: 10.1214/aop/1176995724

Abstract

Let $p_t, t \geqq 0$ be the probability transition semigroup for a continuous one-dimensional diffusion. We examine continuous Markov processes $\xi_s$, defined for all $-\infty < s < \infty$, which are governed by $p_t$. We determine necessary and sufficient conditions for the set of such processes governed by $p_t$ to be nontrivial, and give an example where these conditions are satisfied.

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J. Theodore Cox. "On One-Dimensional Diffusions with Time Parameter Set $(-\infty, \infty)$." Ann. Probab. 5 (5) 807 - 813, October, 1977. https://doi.org/10.1214/aop/1176995724

Information

Published: October, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0376.60078
MathSciNet: MR448587
Digital Object Identifier: 10.1214/aop/1176995724

Subjects:
Primary: 60J60
Secondary: 60J50

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 5 • October, 1977
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