中文摘要：

Lamperti于1961年证明了在适当条件下，半直线上一类近临界的紧邻随机游动经过重整化会弱收敛到布朗运动．考虑过程局部时重整化的极限问题，运用随机游动中的内蕴分枝结构以及非时齐分枝过程重整化极限的结果，证明了其局部时经过适当的重整化会收敛到布朗运动的局部时．

英文摘要：

In 1961, Lamperti proves that a sequence of certain near-critical nearest random walks converges weakly to Brownian motion after proper scaling. Scaling limit in local times is then considered. We prove that local times converge to those of Brownian motion by corresponding scaling. Our proof is based on intrinsic branching structure of random walk and convergence of time in homogeneous branching processe.