【摘要】 研究这样一类复合Poisson过程:S(t)=∑(h(t-Si)Xi)from(i=1 to N(t)),其中N(t)(t>0)是强度为λ>0的齐次Poisson过程,Xi(i≥1)是独立同分布非负随机变量序列,独立于N(t),h(t)(t>0),是非负单调实函数.得到了关于S(t)的大偏差原理和弱收敛.更多还原

【Abstract】 In this paper, the large deviations principle for a class of compound Poisson process S(t)=∑(h(t-Si)Xi)from(i=1 to N(t)) is obtained, where N(t) , t>0, is a homogeneous Poisson process with intensity λ>0, and Xi, i≥1, is i.i.d. nonnegative random variable independent of N(t),while h(t),t>0, is a nonnegative monotone real function. And the weak convergence for S t is also investigated.更多还原