Approximation of quasi-stationary distributions for 1-dimensional killed diffusions with unbounded drifts
Abstract
The long time behavior of an absorbed Markov process is well described by the limiting distribution of the process conditioned to not be killed when it is observed. Our aim is to give an approximation’s method of this limit, when the process is a 1-dimensional Itô diffusion whose drift is allowed to explode at the boundary. We end the paper with two numerical applications: to the logistic Feller diffusion and to the Wright-Fisher diffusion with values in ]0,1[ conditioned to be killed at 0.
Type
Publication
(unsubmitted preprint)
The results of this preprint have been improved significantly in a subsequent work. As a consequence, it will remain unsubmitted. However, the proofs of the present preprint are simpler and can serve as an introduction to the above cited work.
