关键词: 随机环境； 随机游动； 常返性； 瞬时性； L_p收敛

Abstract:

In this paper, the authors describe and analyze a class of random walks with resting state on halfline in  random environments and have a recurrencetransience criterion (including positive recurrence,  zero recurrence, transience); Furthermore, the authors derive an LIL law and L_pconvergence therom by using the approaches of Lyapunov function and martingale.

Key words: Random walks, Random environments, Recurrence; , Transience, L_p convergence.