The Minimal Eigenfunctions Characterize the Ornstein-Uhlenbeck Process
Taylor, J. C.
Ann. Probab., Tome 17 (1989) no. 4, p. 1055-1062 / Harvested from Project Euclid
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A process $(X_t)$ is equivalent to an Ornstein-Uhlenbeck process if and only if $e^{-\lambda t}f(X_t)$ is a martingale for every $f \geq 0$ on $\mathbb{R}^d$ such that $\Delta f(x) - \langle x, \nabla f(x)\rangle = \lambda f(x)$.
Publié le : 1989-07-14
Classification:  Eigenfunctions,  Ornstein-Uhlenbeck process,  characterization,  martingales,  60J60,  60G44 
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     author = {Taylor, J. C.},
     title = {The Minimal Eigenfunctions Characterize the Ornstein-Uhlenbeck Process},
     journal = {Ann. Probab.},
     volume = {17},
     number = {4},
     year = {1989},
     pages = { 1055-1062},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991256}
}

Taylor, J. C. The Minimal Eigenfunctions Characterize the Ornstein-Uhlenbeck Process. Ann. Probab., Tome 17 (1989) no. 4, pp.  1055-1062. http://gdmltest.u-ga.fr/item/1176991256/