TY  - JOUR
TI  - ON THE MOMENTS FOR ERGODIC DISTRIBUTION OF AN INVENTORY MODEL OF TYPE (s, S) WITH REGULARLY VARYING DEMANDS HAVING INFINITE VARIANCE
AB  - In this study a stochastic process X(t) which represents a semi Markovianinventory model of type (s,S) has been considered in the presence of regularly varyingtailed demand quantities. The main purpose of the current study is to investigate theasymptotic behavior of the moments of ergodic distribution of the process X(t) when thedemands have any arbitrary distribution function from the regularly varying subclassof heavy tailed distributions with infinite variance. In order to obtain renewal functiongenerated by the regularly varying random variables, we used a special asymptotic expansion provided by Geluk [14]. As a first step we investigate the current problem withthe whole class of regularly varying distributions with tail parameter 1 <α< 2 ratherthan a single distribution. We obtained a general formula for the asymptotic expressionsof nth order moments (n = 1, 2, 3,...) of ergodic distribution of the process X(t). Subsequently we consider this system with Pareto distributed demand random variables andapply obtained results in this special case.
AU  - KESEMEN, Tülay
AU  - BEKTAŞ KAMIŞLIK, Aslı
AU  - KHANIYEV, Tahir
PY  - 2018
JO  - TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics
VL  - 8
IS  - 2
SN  - 2146-1147
SP  - 318
EP  - 329
DB  - TRDizin
UR  - http://search/yayin/detay/324340
ER  -