Large Deviations for $l^2$-Valued Ornstein-Uhlenbeck Processes
Iscoe, I. ; McDonald, D.
Ann. Probab., Tome 17 (1989) no. 4, p. 58-73 / Harvested from Project Euclid
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A stationary $l^2$-valued Ornstein-Uhlenbeck process given formally by $dX(t) = - AX(t) dt + \sqrt{2a} dB(t)$, where $A$ is a positive self-adjoint constant operator on $l^2$ and $B(t)$ is a cylindrical Brownian motion on $l^2$, is considered. An upper bound on $P(\sup_{t \in \lbrack 0, T \rbrack}\|X(t)\| > x)$ is established and the asymptotics for the given bound, as $x \rightarrow \infty$, is derived.
Publié le : 1989-01-14
Classification:  Ornstein-Uhlenbeck,  Hilbert space,  large deviations,  Dirichlet form,  60H10,  60G17,  60G15 
@article{1176991494,
     author = {Iscoe, I. and McDonald, D.},
     title = {Large Deviations for $l^2$-Valued Ornstein-Uhlenbeck Processes},
     journal = {Ann. Probab.},
     volume = {17},
     number = {4},
     year = {1989},
     pages = { 58-73},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991494}
}

Iscoe, I.; McDonald, D. Large Deviations for $l^2$-Valued Ornstein-Uhlenbeck Processes. Ann. Probab., Tome 17 (1989) no. 4, pp.  58-73. http://gdmltest.u-ga.fr/item/1176991494/