In this paper, we study the existence of global attractor of a class of three-dimensional Brinkman-Forchheimer equation in some unbounded domains which satisfies Poincaré inequality. We use the tail estimation me...In this paper, we study the existence of global attractor of a class of three-dimensional Brinkman-Forchheimer equation in some unbounded domains which satisfies Poincaré inequality. We use the tail estimation method to establish the asymptotic compactness of the solution operator and then prove the existence of the global attractor in(H_0~1(Ω))~3.展开更多
Normal copula with a correlation coefficient between-1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample ...Normal copula with a correlation coefficient between-1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, H¨usler and Reiss(1989) showed that the tail can become asymptotically dependent. We extend this result by deriving the limit of the normalized maximum of n independent observations, where the i-th observation follows from a normal copula with its correlation coefficient being either a parametric or a nonparametric function of i/n. Furthermore, both parametric and nonparametric inference for this unknown function are studied, which can be employed to test the condition by H¨usler and Reiss(1989). A simulation study and real data analysis are presented too.展开更多
基金Supported by the National Natural Science Foundation of China (12001420)。
文摘In this paper, we study the existence of global attractor of a class of three-dimensional Brinkman-Forchheimer equation in some unbounded domains which satisfies Poincaré inequality. We use the tail estimation method to establish the asymptotic compactness of the solution operator and then prove the existence of the global attractor in(H_0~1(Ω))~3.
基金supported by the Simons FoundationNational Natural Science Foundation of China(Grant No.11171275)the Natural Science Foundation Project of CQ(Grant No.cstc2012jj A00029)
文摘Normal copula with a correlation coefficient between-1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, H¨usler and Reiss(1989) showed that the tail can become asymptotically dependent. We extend this result by deriving the limit of the normalized maximum of n independent observations, where the i-th observation follows from a normal copula with its correlation coefficient being either a parametric or a nonparametric function of i/n. Furthermore, both parametric and nonparametric inference for this unknown function are studied, which can be employed to test the condition by H¨usler and Reiss(1989). A simulation study and real data analysis are presented too.
