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Öğe ASYMPTOTIC EXPANSIONS FOR THE MOMENTS OF THE RENEWAL-REWARD PROCESS WITH A NORMAL DISTRIBUTED INTERFERENCE OF CHANCE(Ministry Communications & High Technologies Republic Azerbaijan, 2018) Hanalioglu, Z.; Unver, N. Fescioglu; Khaniyev, T.In this study, a renewal-reward process with a normal distributed interference of chance is mathematically constructed. The ergodicity of this process is discussed. The exact formulas for the nth order moments of the ergodic distribution of the process are obtained, when the interference of chance has a truncated normal distribution with parameters (a, sigma(2)). Using these results, we derive the asymptotic expansions with three terms for the nth order moments of the ergodic distribution, when a -> infinity. Finally, the accuracy of the approximation formulas for the nth order moments of the ergodic distribution are tested by the Monte Carlo simulation method.Öğe ASYMPTOTIC EXPANSIONS FOR THE MOMENTS OF THE RENEWAL-REWARD PROCESS WITH A NORMAL DISTRIBUTED INTERFERENCE OF CHANCE(Institute of Applied Mathematics of Baku State University, 2018) Hanalioglu, Z.; Fescioglu, Unver, N.; Khaniyev, T.In this study, a renewal-reward process with a normal distributed interference of chance is mathematically constructed. The ergodicity of this process is discussed. The exact formulas for the nth order moments of the ergodic distribution of the process are obtained, when the interference of chance has a truncated normal distribution with parameters (a, ?2). Using these results, we derive the asymptotic expansions with three terms for the nth order moments of the ergodic distribution, when a ? ?. Finally, the accuracy of the approximation formulas for the nth order moments of the ergodic distribution are tested by the Monte Carlo simulation method. © 2018, Institute of Applied Mathematics of Baku State University. All rights reserved.Öğe Asymptotic results for an inventory model of type (S, s) with asymmetric triangular distributed interference of chance and delay(Gazi Universitesi, 2018) Hanalioglu, Z.; Khaniyev, T.In this study, a semi – Markovian inventory model of type (s, S) is considered and the model is expressed by a modification of a renewal – reward process (X(t)) with an asymmetric triangular distributed interference of chance and delay. The ergodicity of the process X(t) is proved under some weak conditions. Additionally, exact expressions and three – term asymptotic expansions are found for all the moments of the ergodic distribution. Finally, obtained asymptotic results are compared with exact results for a special case. © 2018, Gazi University Eti Mahallesi. All rights reserved.Öğe Investigation of Upper Bound for the Ruin Probability by Approximate Methods in a Nonlinear Risk Model with Gamma Claims(Institute of Electrical and Electronics Engineers Inc., 2023) Khaniyev, T.; Gever, B.; Hanalioglu, Z.This study considers a non-linear Cramér-Lundberg model of the risk theory and investigates the adjustment coefficient when the claims have gamma distribution. The ruin probability of this non-linear risk model is considered when the premium function is square root of time. Thus, in this study, the adjustment coefficient is explored by numerical methods and proposed an approximate formula for practical calculation of adjustment coefficient. Moreover, an implementation of the obtained approximate formula, which investigates ruin probability, is included as an example at the end of the paper. © 2023 IEEE.Öğe A NOVEL STOCHASTIC APPROACH TO BUFFER STOCK PROBLEM(Turkic World Mathematical Soc, 2024) Hanalioglu, Z.; Poladova, A.; Gever, B.; Khaniyev, T.In this paper, the stochastic fluctuation of buffer stock level at time t is investigated. Therefore, random walk processes X(t) and Y (t) with two specific barriers have been defined to describe the stochastic fluctuation of the product level. Here X(t) equivalent to Y (t) - a and the parameter a specifies half capacity of the buffer stock warehouse. Next, the one-dimensional distribution of the process X(t) has calculated. Moreover, the ergodicity of the process X(t) has been proven and the exact formula for the characteristic function has been found. Then, the weak convergence theorem has been proven for the standardized process W(t) equivalent to X(t)/a, as a -> infinity . Additionally, exact and asymptotic expressions for the ergodic moments of the processes X(t) and Y (t) are obtained.Öğe ON THE BOUNDARY FUNCTIONAL OF THE RANDOM WALK WITH TWO BARRIERS RELATED TO OPTIMAL CAPACITY OF THE BUFFER STOCK(Baku State Univ, Inst Applied Mathematics, 2018) Hanalioglu, Z.; Gever, B.; Poladova, A.; Khaniyev, T.In this study, a boundary functional (N) of the semi-Markovian random walk (X (t)) with two special barriers is considered. The boundary functional N is defined as the first time when the random walk exits from the interval (a). In this study, the boundary functional N has been investigated under the assumption that the jumps of the random walk are expressed by bilateral exponential distributed random variables. There are significant implementations of the boundary functional N in the stock control theory. Especially, it is important to investigate numerical characteristics of the boundary functional N for the finding optimal capacity of buffer stock located between two machines which are working at the same speed. For this reason, the exact expressions for the first three moments of the boundary functional N are obtained by using basic identity for random walk (Feller (1971)). Next, the exact and approximation expressions for the expected value, variance, standard deviation, variation and skewness coefficients of the boundary functional N are derived.Öğe WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE(Turkic World Mathematical Soc, 2015) Hanalioglu, Z.; Khaniyev, T.; Agakishiyev, I.In this study, a semi-Markovian random walk process (X (t)) with a discrete interference of chance is investigated. Here, it is assumed that the zeta(n), n = 1; 2; 3, ..., which describe the discrete interference of chance are independent and identically distributed random variables having restricted normal distribution with parameters (a; sigma(2)). Under this assumption, the ergodicity of the process X (t) is proved. Moreover, the exact forms of the ergodic distribution and characteristic function are obtained. Then, weak convergence theorem for the ergodic distribution of the process W-a (t) = X (t) = a is proved under additional condition that sigma/a -> 0 when a -> infinity.
