Approximation results for the moments of random walk with normally distributed interference of chance
Küçük Resim Yok
Tarih
2023
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Tubitak Scientific & Technological Research Council Turkey
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this study, a random walk process (X (t)) with normally distributed interference of chance is considered. In the literature, this process has been shown to be ergodic and the limit form of the ergodic distribution has been found. Here, unlike previous studies, the moments of the X (t) process are investigated. Although studies investigating the moment problem for various stochastic processes (such as renewal-reward processes) exist in the literature, it has not been considered for random walk processes, as it requires the use of new mathematical tools. Therefore, in this study, firstly, the exact formulas for the first four moments of the ergodic distribution of the X (t) process, which is a modification of the random walk process, are found. Due to the extremely complex mathematical structure of the exact formulas, in the second part of the study, three-term asymptotic expansions are attained for these moments. Based on the asymptotic expansions, simple and useful approximation formulas, for the moments of the process X (t) are proposed. In order to show that the approximate formulas are close enough to the exact formulas, a special example is given at the end of the study and the accuracy of the approximate formulas is examined on this example.
Açıklama
Anahtar Kelimeler
Random walk, discrete interference of chance, ergodic distribution, approximation formulas, normal distribution
Kaynak
Turkish Journal of Mathematics
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
Cilt
47
Sayı
1
