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

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

2006-06-16

arxiv.org/abs/math/0606392v1

J. Appl. Probab. 37, no. 2 (2000), 511-521

Mathematics

Probability

11 pages

Scientific paper

Let $X=(X_t)$ 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 $-(1+\eta)$, with $\eta\in (0,1)$. We prove the existence of a probability measure $\nu$ with a Lebesgue density, depending on $\eta$, such that for every Borel set $A$ of the positive real-line: $\lim_{t\to\infty} P_f(X_t\in A | T_0^X>t)=\nu(A)$, where $T_0^X$ is the hitting time of 0 of $X$.

Affiliated with

Also associated with

No associations

Rating

Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-390286