In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common h...In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.展开更多
According to the problems which the researchers at home and abroad have studied, the article establishes the system of industry cluster model based on the value chain, and analyzes the process of collusion risk evolve...According to the problems which the researchers at home and abroad have studied, the article establishes the system of industry cluster model based on the value chain, and analyzes the process of collusion risk evolved in industry cluster by perturbation theory based on value chain, aiming to find theoretical basis for controlling the evolvement process of collusion risk.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10071081) .
文摘In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.
文摘According to the problems which the researchers at home and abroad have studied, the article establishes the system of industry cluster model based on the value chain, and analyzes the process of collusion risk evolved in industry cluster by perturbation theory based on value chain, aiming to find theoretical basis for controlling the evolvement process of collusion risk.