Some Studies Of One-Dimensional Random Walks In Romdom Environments

The random process in random environments is an active branch in probability. However, the random walks in random environments is its special case. In this article ,we describe and analyze some kinds of random walks in random environments on the line and the right half line . Based some known results,we give several recurrence-transience criteria in a independent but not need identically distributed random environments . Then further study the law of large numbers and center limit theorem in the nonrecurrent .At the same time we also investigate the recurrence and limit theorem for the random walks in time-random environments on the right half line.