A STUDY FOR ERGODICITY AND RECURRENCE OF A MARKOV PROCESS X_(n+1)=f(X_(n))+ε_(n+1)(X_(n))

Abstract

본 논문에서는 X(n+1)=f(X(n))+ε(n+1)f(X(n)) 의 형태를 갖는 Markov 과정이 φ-irreducible 하기위한 조건을 보이고, 이 가정하에서 ergodicity와 recurrence 하기위한 충분조건을 찾는다.;In this thesis, we consider a Markov process {X(n)} on R^(k) of the form X(n+1)=f(X(n))+ε(n+1) f(X(n)). We find the condition under which {X(n)} is φ-irreducible, and under the assumption of φ-irreducibility, we find sufficient conditions for ergodicity and recurrence of the process.