The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary rene...The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary renewal counting process generated by some negatively associated random variables. Using a revised large deviation result of partial sums, the elementary renewal theorem and the central limit theorem of negatively associated random variables, a precise large deviation result is derived for the random sums. The result is applied to the customer-arrival-based insurance risk model. Some uniform asymptotics for the ruin probabilities of an insurance company are obtained as the number of customers or the time tends to infinity.展开更多
Atmospheric carbon dioxide concentration [CO2],incoming solar radiation and sea ice coverage are among the most important factors that control the global climate.By applying the simple cell-to-cell mapping technique t...Atmospheric carbon dioxide concentration [CO2],incoming solar radiation and sea ice coverage are among the most important factors that control the global climate.By applying the simple cell-to-cell mapping technique to a simplified atmosphere-ocean-sea ice feedback climate model,effects of these factors on the stability of the climatic system are studied.The current climatic system is found to be stable but highly nonlinear.The resiliency of stability increases with [CO2] to a summit when [CO2] reaches 290 μL/L which is comparable to the pre-industrial level,suggesting carbon dioxide is essential to the stability of the global climate.With [CO2] rising further,the global climate stability decreases,the mean ocean temperature goes up and the sea ice coverage shrinks in the polar region.When the incoming solar radiation is intensified,the ice coverage gradually diminishes,but the mean ocean temperature remains relatively constant.Overall,our analysis suggests that at the current levels of three external factors the stability of global climate is highly resilient.However,there exists a possibility of extreme states of climate,such as a snow-ball earth and an ice-free earth.展开更多
基金The National Natural Science Foundation of China (No.10671139,11001052)the Natural Science Foundation of Jiangsu Province(No. BK2008284 )+2 种基金China Postdoctoral Science Foundation ( No.20100471365)the Natural Science Foundation of Higher Education Institutions of Jiangsu Province (No. 09KJD110003)Postdoctoral Research Program of Jiangsu Province (No.0901029C)
文摘The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary renewal counting process generated by some negatively associated random variables. Using a revised large deviation result of partial sums, the elementary renewal theorem and the central limit theorem of negatively associated random variables, a precise large deviation result is derived for the random sums. The result is applied to the customer-arrival-based insurance risk model. Some uniform asymptotics for the ruin probabilities of an insurance company are obtained as the number of customers or the time tends to infinity.
基金Funded by the National Natural Science Foundation of China(No.20877105)
文摘Atmospheric carbon dioxide concentration [CO2],incoming solar radiation and sea ice coverage are among the most important factors that control the global climate.By applying the simple cell-to-cell mapping technique to a simplified atmosphere-ocean-sea ice feedback climate model,effects of these factors on the stability of the climatic system are studied.The current climatic system is found to be stable but highly nonlinear.The resiliency of stability increases with [CO2] to a summit when [CO2] reaches 290 μL/L which is comparable to the pre-industrial level,suggesting carbon dioxide is essential to the stability of the global climate.With [CO2] rising further,the global climate stability decreases,the mean ocean temperature goes up and the sea ice coverage shrinks in the polar region.When the incoming solar radiation is intensified,the ice coverage gradually diminishes,but the mean ocean temperature remains relatively constant.Overall,our analysis suggests that at the current levels of three external factors the stability of global climate is highly resilient.However,there exists a possibility of extreme states of climate,such as a snow-ball earth and an ice-free earth.
