The Annals of Probability

Further Results on One-dimensional Diffusions with Time Parameter set S(- \infty, \infty)$

J. Theodore Cox

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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.

Article information

Source
Ann. Probab., Volume 7, Number 3 (1979), 537-542.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995054

Digital Object Identifier
doi:10.1214/aop/1176995054

Mathematical Reviews number (MathSciNet)
MR528331

Zentralblatt MATH identifier
0401.60073

JSTOR
links.jstor.org

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60J50: Boundary theory

Keywords
One-dimensional diffusion boundary first passage time entrance laws

Citation

Cox, J. Theodore. Further Results on One-dimensional Diffusions with Time Parameter set S(- \infty, \infty)$. Ann. Probab. 7 (1979), no. 3, 537--542. doi:10.1214/aop/1176995054. https://projecteuclid.org/euclid.aop/1176995054


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