On One-Dimensional Diffusions with Time Parameter Set $(-\infty, \infty)$
Cox, J. Theodore
Ann. Probab., Tome 5 (1977) no. 6, p. 807-813 / Harvested from Project Euclid
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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.
Publié le : 1977-10-14
Classification:  One-dimensional diffusions,  boundary,  entrance laws,  60J60,  60J50 
@article{1176995724,
     author = {Cox, J. Theodore},
     title = {On One-Dimensional Diffusions with Time Parameter Set $(-\infty, \infty)$},
     journal = {Ann. Probab.},
     volume = {5},
     number = {6},
     year = {1977},
     pages = { 807-813},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995724}
}

Cox, J. Theodore. On One-Dimensional Diffusions with Time Parameter Set $(-\infty, \infty)$. Ann. Probab., Tome 5 (1977) no. 6, pp.  807-813. http://gdmltest.u-ga.fr/item/1176995724/