We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoti...We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoting the counting measure of particles of generation n, and Eξ the conditional expectation given the environment ξ. We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W, when W is non-degenerate.展开更多
An entropy-based statistic TpE has been proposed for genomic association study for disease-susceptibility locus. The statistic TpE may be directly adopted and/or extended to quantitative-trait locus （QTL）mapping for...An entropy-based statistic TpE has been proposed for genomic association study for disease-susceptibility locus. The statistic TpE may be directly adopted and/or extended to quantitative-trait locus （QTL）mapping for quantitative traits. In this article, the statistic TpE was extended and applied to quantitative trait for association analysis of QTL by means of selective genotyping. The statistical properties （the type I error rate and the power） were examined under a range of parameters and population-sampling strategies （e.g., various genetic models, various heritabilities, and various sample-selection threshold values） by simulation studies. The results indicated that the statistic TpE is robust and powerful for genomic association study of QTL. A simulation study based on the haplotype frequencies of 10 single nucleotide polymorphisms （SNPs） of angiotensin-I converting enzyme genes was conducted to evaluate the performance of the statistic TPE for genetic association study.展开更多
In this paper, we study a risk model with two independent classes of risks, in which both claim number processes are renewal processes with phasetype inter-arrival times. Using a generalized matrix Dickson-Hipp operat...In this paper, we study a risk model with two independent classes of risks, in which both claim number processes are renewal processes with phasetype inter-arrival times. Using a generalized matrix Dickson-Hipp operator, a matrix Volterra integral equation for the Gerber-Shiu function is derived. And the analytical solution to the Gerber-Shiu function is also provided.展开更多
基金benefited from the support of the French government Investissements d’Avenir program ANR-11-LABX-0020-01partially supported by the National Natural Science Foundation of China(11571052,11401590,11731012 and 11671404)by Hunan Natural Science Foundation(2017JJ2271)
文摘We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoting the counting measure of particles of generation n, and Eξ the conditional expectation given the environment ξ. We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W, when W is non-degenerate.
文摘An entropy-based statistic TpE has been proposed for genomic association study for disease-susceptibility locus. The statistic TpE may be directly adopted and/or extended to quantitative-trait locus （QTL）mapping for quantitative traits. In this article, the statistic TpE was extended and applied to quantitative trait for association analysis of QTL by means of selective genotyping. The statistical properties （the type I error rate and the power） were examined under a range of parameters and population-sampling strategies （e.g., various genetic models, various heritabilities, and various sample-selection threshold values） by simulation studies. The results indicated that the statistic TpE is robust and powerful for genomic association study of QTL. A simulation study based on the haplotype frequencies of 10 single nucleotide polymorphisms （SNPs） of angiotensin-I converting enzyme genes was conducted to evaluate the performance of the statistic TPE for genetic association study.
文摘In this paper, we study a risk model with two independent classes of risks, in which both claim number processes are renewal processes with phasetype inter-arrival times. Using a generalized matrix Dickson-Hipp operator, a matrix Volterra integral equation for the Gerber-Shiu function is derived. And the analytical solution to the Gerber-Shiu function is also provided.
