标题： 分支对称Hunt过程的大数定律与测度值分支率 显示英文标题

标题： Law of large numbers for branching symmetric Hunt processes with measure-valued branching rates

摘要： 我们为一类分支对称Hunt过程建立了弱大数定律和强大数定律，其中分支率为相对于基础Hunt过程的光滑测度，分支机制为一般且与状态相关的。 我们的工作受到Chen-Shiozawa [J. Funct. Anal., 250, 374--399, 2007]关于分支对称马尔可夫过程的强大数定律近期研究以及Engländer-Harris-Kyprianou [Ann. Inst. Henri Poincaré Probab. Stat., 46, 279--298, 2010]关于分支扩散的研究的启发。 我们的结果可以应用于一些有趣的例子，这些例子未被上述论文涵盖。 显示英文摘要

摘要： We establish weak and strong law of large numbers for a class of branching symmetric Hunt processes with the branching rate being a smooth measure with respect to the underlying Hunt process, and the branching mechanism being general and state-dependent. Our work is motivated by recent work on strong law of large numbers for branching symmetric Markov processes by Chen-Shiozawa [J. Funct. Anal., 250, 374--399, 2007] and for branching diffusions by Engl\"ander-Harris-Kyprianou [Ann. Inst. Henri Poincar\'e Probab. Stat., 46, 279--298, 2010]. Our results can be applied to some interesting examples that are covered by neither of these papers.