2009/05/22 by Denis Villemonais, Villemonais, Denis · 4 citations
Economics, Econometrics and Finance · Mathematics · #60J60 #60K35 #65C50 #Applied mathematics #FOS: Mathematics #Mathematics #Physics #Probability (math.PR) #Statistical physics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories #math.PR #msc:60J60 #msc:60K35 #msc:65C50
paper · pdf · doi:10.48550/arxiv.0905.3636
published in arXiv (Cornell University) (Cornell University)
arxiv created 2009/05/22 · openalex publication_date 2009/05/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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. In a first step, we show how to restrict the study to the case of a diffusion with values in a bounded interval and whose drift is bounded. In a second step, we show an approximation method of the limiting conditional distribution of such diffusions, based on a Fleming-Viot type interacting particle system. 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.