LIU XiJun, YU ChangJun, . Asymptotics for a Type of Randomly Weighted Sums and Its Application[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(2): 145-155.
Citation:
LIU XiJun, YU ChangJun, . Asymptotics for a Type of Randomly Weighted Sums and Its Application[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(2): 145-155.
LIU XiJun, YU ChangJun, . Asymptotics for a Type of Randomly Weighted Sums and Its Application[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(2): 145-155.
Citation:
LIU XiJun, YU ChangJun, . Asymptotics for a Type of Randomly Weighted Sums and Its Application[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(2): 145-155.
This paper considers the asymptotics of randomly weighted sums and their maxima, where the increments {X_i,i\geq1\} is a sequence of independent, identically distributed and real-valued random variables and the weights {\theta_i,i\geq1\} form another sequence of non-negative and independent random variables, and the two sequences of random variables follow some dependence structures. When the common distribution F of the increments belongs to dominant variation class, we obtain some weakly asymptotic estimations for the tail probability of randomly weighted sums and their maxima. In particular, when the F belongs to consistent variation class, some asymptotic formulas is presented. Finally, these results are applied to the asymptotic estimation for the ruin probability.