Investigation of a random walk with generalized reflecting barrier

In this thesis, a random walk with a generalized reflecting barrier mathematically constructed and is investigated with analytic and asymptotic methods. After examining the one dimensional distribution of the process, the general ergodic theorem for the process is proved. Both the ergodic distribution and its characteristic function are obtained in this section. Next, the weak convergence theorem for the process is proved and the limit form of the ergodic distribution of the process is found. In the following chapter, the convergence rate of this limit distribution of the process is calculated and a quite practical formula is obtained. Moreover, for some boundary functionals of the process, the exact expression for the expected value and variance are obtained. Also, for some moments for the boundary functionals, the asymptotic expansions are calculated. With the help of these expressions, the exact expressions and asymptotic expansions for the ergodic moments of the process are obtained. Consecutively, the obtained formulae are applied to a problem.