作者：CHAUVIN, B
摘要：For a branching Brownian motion, a probability space of trees is defined. By analogy with stopping times on R, stopping lines are defined to get a general branching property. We exhibit an intrinsic class of martingales which are products indexed by the elements of a stopping line. We prove that all these martingales have the same limit which we identify. Two particular cases arise: the line of particles living at time t and the first crossings of a straight line whose equation is y = at - x i...
作者：DONNELLY, P
摘要：We derive conditions under which a sequence of processes will converge to a (continuous-time) Markov chain with an entrance boundary. Our main application of this result is in proving weak convergence of the so-called population ancestral processes, associated with a wide class of exchangeable reproductive models, to a particular death process with an entrance boundary at infinity. This settles a conjecture of Kingman. We also prove weak convergence of the absorption times of many neutral gene...
作者：RACHEV, ST; RUSCHENDORF, L
作者单位：University of Munster
摘要：Let zeta be chosen at random on the surface of the p-sphere in R(n), Op,n : = {x is-an-element-of R(n): SIGMA-i = 1n \x(i)\p = n}. If p = 2, then the first k components zeta-1,...,zeta-k are, for k fixed, in the limit as n --> infinity independent standard normal. Considering the general case p > 0, the same phenomenon appears with a distribution F(p) in an exponential class E. F(p) can be characterized by the distribution of quotients of sums, by conditional distributions and by a maximum ent...
