The influence of non-uniqueness in selecting statistical time ranges on seismicity parameters of b value and annual mean occurrence rate ν4 is widely analyzed and studied. The studied result states that the influence...The influence of non-uniqueness in selecting statistical time ranges on seismicity parameters of b value and annual mean occurrence rate ν4 is widely analyzed and studied. The studied result states that the influence of statistical time range on the b value is generally smaller than on the annual mean rate. Owing to the exponentially functional relation between the annual mean rate and b value, the variation of b value by varying statistical time range brings about decrease or increase in the annual mean rates of each magnitude interval with power progression law. These results will exert a synthetic effect on seismic safety evaluation results in various regions in our country.展开更多
Let {Xn,n ≥ 0} be an AR（1） process. Let Q（n） be the rescaled range statistic, or the R/S statistic for {Xn} which is given by （max1≤k≤n（∑j=1^k（Xj - ^-Xn）） - min 1≤k≤n（∑j=1^k（ Xj - ^Xn ））） /（n ^-...Let {Xn,n ≥ 0} be an AR（1） process. Let Q（n） be the rescaled range statistic, or the R/S statistic for {Xn} which is given by （max1≤k≤n（∑j=1^k（Xj - ^-Xn）） - min 1≤k≤n（∑j=1^k（ Xj - ^Xn ））） /（n ^-1∑j=1^n（Xj -^-Xn）^2）^1/2 where ^-Xn = n^-1 ∑j=1^nXj. In this paper we show a law of iterated logarithm for rescaled range statistics Q（n） for AR（1） model.展开更多
基金Chinese Joint Seismological Science Foundation (100110).
文摘The influence of non-uniqueness in selecting statistical time ranges on seismicity parameters of b value and annual mean occurrence rate ν4 is widely analyzed and studied. The studied result states that the influence of statistical time range on the b value is generally smaller than on the annual mean rate. Owing to the exponentially functional relation between the annual mean rate and b value, the variation of b value by varying statistical time range brings about decrease or increase in the annual mean rates of each magnitude interval with power progression law. These results will exert a synthetic effect on seismic safety evaluation results in various regions in our country.
基金supported by NSFC(10071072) supported by SRFDP(200235090)+1 种基金support by the BK21 Project of the Department of Mathematics,Yonsei Universitythe Interdisciplinary Research Program of KOSEF 1999-2-103-001-5 and com2MaC in POSTECH
文摘Let {Xn,n ≥ 0} be an AR（1） process. Let Q（n） be the rescaled range statistic, or the R/S statistic for {Xn} which is given by （max1≤k≤n（∑j=1^k（Xj - ^-Xn）） - min 1≤k≤n（∑j=1^k（ Xj - ^Xn ））） /（n ^-1∑j=1^n（Xj -^-Xn）^2）^1/2 where ^-Xn = n^-1 ∑j=1^nXj. In this paper we show a law of iterated logarithm for rescaled range statistics Q（n） for AR（1） model.
