Asymptotic rate forweak convergence of the distribution of renewal-reward process with a generalized reflecting barrier

Xanıyev T., Gever B., Hanalioglu Z.

3rd Applied Mathematics and Approximation Theory, AMAT 2015, Ankara, Turkey, 28 - 31 May 2015, vol.441, pp.313-331, (Full Text) identifier

  • Nəşrin Növü: Conference Paper / Full Text
  • Cild: 441
  • Doi nömrəsi: 10.1007/978-3-319-30322-2_22
  • Çap olunduğu şəhər: Ankara
  • Ölkə: Turkey
  • Səhifə sayı: pp.313-331
  • Açıq Arxiv Kolleksiyası: Konfrans Materialı
  • Adres: Bəli

Qısa məlumat

In this study, a renewal-reward process (X(t)) with a generalized reflecting barrier is constructed mathematically and under some weak conditions, the ergodicity of the process is proved. The explicit form of the ergodic distribution is found and after standardization, it is shown that the ergodic distribution converges to the limit distribution R(x), when λ→∞, i.e., (Formula presented.) Here, F(x) is the distribution function of the initial random variables {ηn}, n =1, 2, …, which express the amount of rewards and m2 ≡ E(η2 1). Finally, to evaluate asymptotic rate of the weak convergence, the following inequality is obtained: (Formula presented.). Here, (Formula presented.) is the limit distribution of residual waiting time generated by {ηn}, n = 1, 2, …, and m1 = E(η1).