The Limit Properties For Multi-dimension Random Walks In Random Sceneries

The limit theory is one of important parts of research for probability. It. has a lot of fields of application, and is significant bases of other branches. The problem of research for stochastic processes and random variables in random sceneries is one of hot part of probability, and very active both home and abroad. This master thesis mainly study the properties of almost everywhere limit for multi-dimensions random walkes and its dependent process in random sceneries.On the basic of haven results, this master thesis proves the laws of large num-bers for d-dimension random walks in random sceneries, and gives large deviation and a law of the iterated logarithm for two-dimension additive stable processes in random scenery, and improves some haven results. It consists of three chapters as follows:Chapter one introduces the definitions of some common stochastic processes, the development of the limit theory of probability and the original background of random walk in random scenery, and the main work of this thesis.Chapter two proves a law of large number for d-dimension random walk in random scenery used the method of estimating moments and tail, and gives its an equal result, which improves some haven results for one dimension random walks in random sceneries.Chapter three studies the speed of convergence for two-dimension additive stable processes in random scenery with the properties of Brownian motion and additive stable processes, and gets its large deviation and iterated logarithm, whieh improves some haven results.