Ph.D. Tezi Görüntüleme

Student:	Tulay KESEMEN
Supervisor:	Prof. Dr. Tahir KHANIYEV
Department:	Mathematics
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University, Turkey

Title of the Thesis:	Investigation of extended models of type (s,S) with random volume by analytic and asymptotic methods
Level:	Ph.D.
Acceptance Date:	24/11/2006
Number of Pages:	118
Registration Number:	Di574

Summary:

Under some weak assumptions the ergodicity of this process is discussed and function of ergodic distribution of this process is found explicitly.

In addition to these, the characteristic function of ergodic distribution of this process is expressed by means of boundary functional S[N(z)]. Exact formulas for the first four moments of ergodic distribution of this process are obtained by using them when the random variable zeta1 has an exponential distribution with lamda>0 parameter, Erlang distribution with second and third order, Gamma distribution with (alpha, lamda) parameter. Moreover, based on the above results, asymptotic result for the first four moments and skewness, kurtosis of ergodic distribution of process are obtained when the random variable zeta1 has an exponential distribution with lamda>0 parameter, Erlang distribution with second and third order, Gamma distribution with (alpha, lamda) parameter as lamda-->0.

At the same time, weak convergence theorem is also given for the process when the random variable zeta1 has an exponential distribution with lamda>0 parameter.

Key Words: Renewal Process, Random Walk Process, Semi-Markov Random Walk Process, Boundary Functional, Additive Functional, Wald Identity, Spitzer Identity, Ladder Variables, Weak Convergence, Asymptotic Behaviour.