Examining a semi-markovian random walk with pareto distributed interference of chance by using asymptotic methods

In this thesis ''Examining a semi-Markovian random walk with Pareto distributed interference of chance by using asymptotic methods'' is considered. The stochastic process under consideration is constructed mathematically and, under some general conditions the ergodicity of the process is discussed. Besides the ergodic distribution function and, the ergodic characteristic function is expressed by using border functional S_N(z) . Furthermore by using them, the exact formulas for the first four stationary moments of the ergodic distirbution of the process X(t) is obtained. By using the obtained asymptotic expansion, to observe the adequateness of calculated moments to the exact values, a special case is considered and by using Monte Carlo simulation method some formulas is obtained for ergodic moments and they are compared with asymptotic results. As a result of comparison it is observed that the obtained asymptotic expansions are close enough to the simulation results. Finally the weak convergence theorem for the ergodic expansion of this process is proved.