Limit Properties For Finite-dimensional Irreducibility Random Walks In Random Environments And Its Application

In this paper, a class of the irreducible random walk on the definition in the integer lattice Zm under conditions in the stationary ergodic is discussed by using the transition probability of Markov and the limit line of permutation operator. By the application of its results, there are being promoted as well. All content is divided into five Chapters:As the introduction, in Chapter1, the background of some special random walk and the main work of the paper are briefly described.Chapter2is preliminaries section, the basic knowledge about convergence in proba-bility, recurrence and irreducibility which will be used in this work is provided.Chapter3, limit properties of the irreducible random walks in the integer lattice Zm under conditions of the time random environment ζ(n)={(ζn=x+ξ1+ξ2+…+ξn,n≥1} is considered. By constructing the Green’s function of transition probability, stationary and ergodicity defined as ζn(n≥1) in time random environment. For a weaker conditions when E|ξ1|<∞, Eξ12<∞, VARζ(n)ξn<∞, the following conditions must be satisfied: Then for n→∞iff, a similar result of the weak law of large numbers in normal conditions be obtained.And then in the space of{Ω,(?)}, we made a range of segmentation about Column set algebra on the set function P’(C)={Px1x2…xn(Bn),n∈N+,xn∈X,Bn∈(?)n}. Then the irreducible random walks ξn is mapped to the coordinates of each other interval, the limit properties of which set function are studied in depth. Finally, we got a similar functional strong limit theorems of the Markov limit theorem.In Chapter4, the model of finite-dimensional irreducibility random walks of order2is studied. Given ω, of which must be satisfied: For n≥1, j≥1, then Through its recurrence rule discussed, by constructing permutation operator of transition probability as following: Then by means of the classical Kronecker strong law of large numbers and the Linderberg-Feller central limit theorem, we got the corresponding strong law of large numbers and central limit theorem eventually.In Chapter5, we mainly focuses on the strong asymptotic results of the extremal irreducible random walks on random intervals. Under the sub-index distributions of family conditions to the amount claimed surplus level and its bankruptcy probability r(x)={P(MΨ>x),MΨ=max{unΨ, n≥1}} are being studied. Then proved an asymptotic result of the bankruptcy probability.In summary, limit properties of two types about special finite-dimensional irreducibil-ity random walks is studied on the basis of theorems about some random walks. The results are not only extended some known ones about random walks theory, but also given a new theoretical significance for finite-dimensional irreducibility random walks of order2as well.