%0 Journal Article %1 arthreya2005branchingcoalescing %A Athreya, Siva R. %A Swart, Jan M %C Berlin / Heidelberg %D 2005 %I Springer %J Probability Theory and Related Fields %K Wright-Fisher_diffusion ancestral_selection_graph branching_random_walk coalescent_theory duality ergodicity spatial_structure %N 3 %P 376-414 %R 10.1007/s00440-004-0377-4 %T Branching-coalescing particle systems %U http://dx.doi.org/10.1007/s00440-004-0377-4 %V 131 %X We study the ergodic behavior of systems of particles performing independent random walks, binary splitting, coalescence and deaths. Such particle systems are dual to systems of linearly interacting Wright-Fisher diffusions, used to model a population with resampling, selection and mutations. We use this duality to prove that the upper invariant measure of the particle system is the only homogeneous nontrivial invariant law and the limit started from any homogeneous nontrivial initial law. An erratum to this article is available at http://dx.doi.org/10.1007/s00440-009-0232-8. (corrects Theorem 7)

@article{arthreya2005branchingcoalescing, abstract = {We study the ergodic behavior of systems of particles performing independent random walks, binary splitting, coalescence and deaths. Such particle systems are dual to systems of linearly interacting Wright-Fisher diffusions, used to model a population with resampling, selection and mutations. We use this duality to prove that the upper invariant measure of the particle system is the only homogeneous nontrivial invariant law and the limit started from any homogeneous nontrivial initial law. An erratum to this article is available at http://dx.doi.org/10.1007/s00440-009-0232-8. (corrects Theorem 7)}, added-at = {2011-03-06T07:55:25.000+0100}, address = {Berlin / Heidelberg}, affiliation = {Indian Statistical Institute 8th mile Mysore Road RV College PO Bangalore -560059 India}, author = {Athreya, Siva R. and Swart, Jan M}, biburl = {https://www.bibsonomy.org/bibtex/2e5b16933faea7f41714c93ae8bfb22dc/peter.ralph}, doi = {10.1007/s00440-004-0377-4}, interhash = {2ee97e37894a5dd09a8c2a17dab2996e}, intrahash = {e5b16933faea7f41714c93ae8bfb22dc}, issn = {0178-8051}, journal = {Probability Theory and Related Fields}, keyword = {Mathematics and Statistics}, keywords = {Wright-Fisher_diffusion ancestral_selection_graph branching_random_walk coalescent_theory duality ergodicity spatial_structure}, number = 3, pages = {376-414}, publisher = {Springer}, timestamp = {2013-12-14T06:12:18.000+0100}, title = {Branching-coalescing particle systems}, url = {http://dx.doi.org/10.1007/s00440-004-0377-4}, volume = 131, year = 2005 }