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
Mammalian carnivores are rarely considered for environmental reconstructions because they are extremely adaptable and their geographic range is usually large. However, the functional morphology of carnivore long bones...Mammalian carnivores are rarely considered for environmental reconstructions because they are extremely adaptable and their geographic range is usually large. However, the functional morphology of carnivore long bones can be indicative of locomotor behaviour as well as adaptation to specific kind of habitats. Here, different long bone ratios belonging to a subsample of extant large carnivores are used to infer palaeoecology of a comparative sample of Plio-Pleistocene fossils belonging to Italian paleo-communities. A multivariate long bone shape space reveals similarities between extant and fossil carnivores and multiple logistic regression models suggest that specific indices （the brachial and the Mt/F） can be applied to predict adaptations to grassland and tropical biomes. These functional indices exhibit also a phylogenetic signal to different degree. The brachial index is a significant predictor of adaptations to tropical biomes when phylogeny is taken into account, while Mt/F is not correlated anymore to habitat adaptations. However, the proportion of grassland-adapted carnivores in Italian paleo-communities exhibits a negative relationship with mean oxygen isotopic values, which are indicative of past climatic oscillations. As climate became more unstable during the Ice Ages, large carnivore guilds from the Italian peninsula were invaded by tropical/closed-adapted species. These species take advantage of the temperate forest cover that was more spread after 1.0 Ma than in the initial phase of the Quaternary （2.0 Ma） when the climate was more arid [Current Zoology 57 （3）： 269-283, 2011].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Mammalian carnivores are rarely considered for environmental reconstructions because they are extremely adaptable and their geographic range is usually large. However, the functional morphology of carnivore long bones can be indicative of locomotor behaviour as well as adaptation to specific kind of habitats. Here, different long bone ratios belonging to a subsample of extant large carnivores are used to infer palaeoecology of a comparative sample of Plio-Pleistocene fossils belonging to Italian paleo-communities. A multivariate long bone shape space reveals similarities between extant and fossil carnivores and multiple logistic regression models suggest that specific indices （the brachial and the Mt/F） can be applied to predict adaptations to grassland and tropical biomes. These functional indices exhibit also a phylogenetic signal to different degree. The brachial index is a significant predictor of adaptations to tropical biomes when phylogeny is taken into account, while Mt/F is not correlated anymore to habitat adaptations. However, the proportion of grassland-adapted carnivores in Italian paleo-communities exhibits a negative relationship with mean oxygen isotopic values, which are indicative of past climatic oscillations. As climate became more unstable during the Ice Ages, large carnivore guilds from the Italian peninsula were invaded by tropical/closed-adapted species. These species take advantage of the temperate forest cover that was more spread after 1.0 Ma than in the initial phase of the Quaternary （2.0 Ma） when the climate was more arid [Current Zoology 57 （3）： 269-283, 2011].
