%0 Journal Article %1 seneta1966quasistationary %A Seneta, E. %D 1966 %J J. Roy. Statist. Soc. Ser. B %K Wright-Fisher_model diffusion_approximation quasistationarity %P 253--277 %T Quasi-stationary distributions and time-reversion in genetics. (With discussion) %U http://www.jstor.org/stable/2984371 %V 28 %X Finite absorbing Markov chains appear frequently as models for genetic processes. Although in such chains absorption in a finite time is certain, this time may be long, and it is then of interest to consider quasi-stationary distributions as describing the process in such situations; this is also true of certain infinite chains. Two such distributions are discussed, and derived for three particular genetic models as diffusion approximations. The distribution regarded as more satisfactory has interesting properties as regards `time-reversion' of the genetic process. A general discussion of this concept leads to the quasi-stationary generalization of Wright's formula for stationary distributions.

@article{seneta1966quasistationary, abstract = {Finite absorbing Markov chains appear frequently as models for genetic processes. Although in such chains absorption in a finite time is certain, this time may be long, and it is then of interest to consider quasi-stationary distributions as describing the process in such situations; this is also true of certain infinite chains. Two such distributions are discussed, and derived for three particular genetic models as diffusion approximations. The distribution regarded as more satisfactory has interesting properties as regards `time-reversion' of the genetic process. A general discussion of this concept leads to the quasi-stationary generalization of Wright's formula for stationary distributions.}, added-at = {2012-12-14T00:33:18.000+0100}, author = {Seneta, E.}, biburl = {https://www.bibsonomy.org/bibtex/2abbfa780cf3ce1feddf55658e61bd531/peter.ralph}, fjournal = {Journal of the Royal Statistical Society. Series B. Methodological}, interhash = {a13c436086f30bb74656567f67273a82}, intrahash = {abbfa780cf3ce1feddf55658e61bd531}, issn = {0035-9246}, journal = {J. Roy. Statist. Soc. Ser. B}, keywords = {Wright-Fisher_model diffusion_approximation quasistationarity}, mrclass = {60.65 (92.20)}, mrnumber = {0202192 (34 \#2065)}, mrreviewer = {D. G. Kendall}, pages = {253--277}, timestamp = {2012-12-14T00:33:18.000+0100}, title = {Quasi-stationary distributions and time-reversion in genetics. ({W}ith discussion)}, url = {http://www.jstor.org/stable/2984371}, volume = 28, year = 1966 }