A strong law of large numbers for branching processes: almost sure spine events
@article{ECP2641, author = {Simon Harris and Matthew Roberts}, title = {A strong law of large numbers for branching processes: almost sure spine events}, journal = {Electron. Commun. Probab.}, fjournal = {Electronic Communications in Probability}, volume = {19}, year = {2014}, keywords = {branching processes, spines, martingales, strong law}, abstract = {}, pages = {no. 28, 1-6}, issn = {1083-589X}, doi = {10.1214/ECP.v19-2641}, url = {http://ecp.ejpecp.org/article/view/2641}}We demonstrate a novel strong law of large numbers for branching processes, with a simple proof via measure-theoretic manipulations and spine theory. Roughly speaking, any sequence of events that eventually occurs almost surely for the spine entails the almost sure convergence of a certain sum over particles in the population.