ON THE DISTRIBUTION OF THE MAXIMUM OF SUMS OF A SEQUENCE OF INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES.

Yıl 2016, Cilt: 6 Sayı: 1, 70 - 74, 01.06.2016

T. M .aliyev Sh. B. Bakhshiyev

Öz

The authors find in terms of generating functions the distribution of the maximum of sums of independent and identically distributed random variables with no negative jumps different from −1.

Anahtar Kelimeler

random walk, Laplace transform, generating function.

Kaynakça

• Nelson,R., (1995), Probability, stochastic processes and queening theory: the mathematics of computer performance modeling, Springer- Verlag, Inc. New York, pp. 583.
• Korshunov,DA., (2006), On the distribution density of the supremum of a random walk in the subex- ponential case. Siberian Mathematical Journal, Vol.74, No.6, pp. 1296-1302. (in Russian)
• Yezhov,I.I., Kadankov,V.F. and Kadankova,T.V., (2007), Main two-boundary problems for a random walk. ISSN 1027-3190. Ukrainian Mathematical Journal, Vol.59, No.11, pp. 1485-1509. (in Russian)
• Nasirova,T. I. and Aliyev,T.M., (2011), Probability. Monograph (in Azerbaijani). Baku, pp. 178.
• Tofiq Aliyev, for a photograph and biography, see TWMS Journal of Applied and Engineering Mathematics, Volume 4, No.2, 2014.