We consider a strong Markov process with killing and prove an approximation method for the distribution of the process conditioned not to be killed when it is observed. The method is based on a Fleming-Viot type particle system with rebirths, whose particles evolve as independent copies of the original strong Markov process and jump onto each others instead of being killed. Our only assumption is that the number of rebirths of the Fleming-Viot type system doesn't explode in finite time almost surely and that the survival probability of the original process remains positive in finite time. The approximation method generalizes previous results and comes with a speed of convergence. A criterion for the non-explosion of the number of rebirths is also provided for general systems of time and environment dependent diffusion particles. This includes, but is not limited to, the case of the Fleming-Viot type system of the approximation method. The proof of the non-explosion criterion uses an original non-attainability of (0,0) result for pair of non-negative semi-martingales with positive jumps.
Mots clés : particle systems, conditional distributions
@article{PS_2014__18__441_0,
author = {Villemonais, Denis},
title = {General approximation method for the distribution of {Markov} processes conditioned not to be killed},
journal = {ESAIM: Probability and Statistics},
pages = {441--467},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2013045},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2013045/}
}
TY - JOUR AU - Villemonais, Denis TI - General approximation method for the distribution of Markov processes conditioned not to be killed JO - ESAIM: Probability and Statistics PY - 2014 SP - 441 EP - 467 VL - 18 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2013045/ DO - 10.1051/ps/2013045 LA - en ID - PS_2014__18__441_0 ER -
%0 Journal Article %A Villemonais, Denis %T General approximation method for the distribution of Markov processes conditioned not to be killed %J ESAIM: Probability and Statistics %D 2014 %P 441-467 %V 18 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2013045/ %R 10.1051/ps/2013045 %G en %F PS_2014__18__441_0
Villemonais, Denis. General approximation method for the distribution of Markov processes conditioned not to be killed. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 441-467. doi : 10.1051/ps/2013045. http://www.numdam.org/articles/10.1051/ps/2013045/
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