Paper
Law of iterated logarithm for supercritical non-symmetric branching Markov process
Authors
Haojie Hou, Yan-Xia Ren, Renming Song
Abstract
Let be a supercritical branching Markov process (which is not necessary symmetric) on a locally compact metric measure space with spatially dependent local branching mechanism. Under some assumptions on the semigroup of the spatial motion, we first prove law of iterated logarithm type results for under the second moment condition on the branching mechanism, where is a linear combination of eigenfunctions of the mean semigroup of . Then we prove law of iterated logarithm type results for under the fourth moment condition, where belongs to a larger class of functions.