Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process

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dc.creatorLladser, Manuel
dc.creatorMartin, Jaime San
dc.date2006-06-16
dc.date.accessioned2026-07-07T08:07:54Z
dc.date.available2026-07-07T08:07:54Z
dc.descriptionLet $X=(X_t)$ be a one-dimensional Ornstein-Uhlenbeck process with an initial density function $f$ supported on the positive real-line that is a regularly varying function with exponent $-(1+η)$, with $η\in (0,1)$. We prove the existence of a probability measure $ν$ with a Lebesgue density, depending on $η$, such that for every Borel set $A$ of the positive real-line: $\lim_{t\to\infty} P_f(X_t\in A | T_0^X>t)=ν(A)$, where $T_0^X$ is the hitting time of 0 of $X$.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0606392
dc.identifierhttp://arxiv.org/abs/math/0606392
dc.identifierJ. Appl. Probab. 37, no. 2 (2000), 511-521
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131089
dc.subjectProbability
dc.subjectMathematical Physics
dc.subjectStatistics Theory
dc.subject60H10; 65C30
dc.titleDomain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process
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