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By decomposing the random walk path, we construct a multitype branchingprocess with immigration in random environment for corresponding random walkwith bounded jumps in random environment. Then we give two applications of thebranching structure. Firstly, we specify the explicit invariant density by amethod different with the one used in Br\'emont [3] and reprove the law oflarge numbers of the random walk by a method known as the environment viewedfrom particles". Secondly, the branching structure enables us to prove a stablelimit law, generalizing the result of Kesten-Kozlov-Spitzer [11] for thenearest random walk in random environment. As a byproduct, we also prove thatthe total population of a multitype branching process in random environmentwith immigration before the first regeneration belongs to the domain ofattraction of some \kappa -stable law.

Branching structure for an (L-1) random walk in random environment and its applications