分枝过程和超过程是研究粒子群体在一定的环境下发展演化的数学模型，在分枝过程或超过程中加入竞争机制，便得到所谓的带竞争的分枝过程或超过程。首先我们将用随机方程分别构造离散状态和连续状态的带竞争的分枝过程，研究它们之间的极限问题；然后用随机方程构造一些带竞争的分枝粒子系统，研究其重整化之后到带竞争的超过程的收敛问题。

Branching processes and superprocesses are the mathematical models for populations evolving randomly in certain environments. To join the competition in branching processes or superprocesses, we get the so-called branching processes with competition or superprocesses with competition. First we will construct branching processes with competition, in both discrete and continuous-state space, by stochastic equations and study their scaling limit problems. Then we will use stochastic equations to construct some branching particle systems with competition and show that after suitable renormalization they can converge to some superprocesses with competition.