An explicit and recursive representation is presented for moments of the first hitting times of birth-death processes on trees. Based on that, the criteria on ergodicity, strong ergodicity, and l-ergodicity of the pro...An explicit and recursive representation is presented for moments of the first hitting times of birth-death processes on trees. Based on that, the criteria on ergodicity, strong ergodicity, and l-ergodicity of the processes as well as a necessary condition for exponential ergodicity are obtained.展开更多
Qiyechangbai and Hadacongl were used to study the relationship of the leaf age of overwinter to bolting and, returning green by the difference of sowing time. The results showed that the earlier the seeds were sown, t...Qiyechangbai and Hadacongl were used to study the relationship of the leaf age of overwinter to bolting and, returning green by the difference of sowing time. The results showed that the earlier the seeds were sown, the older leaf age of overwinter was, the higher the rates of returning green and bolting rate were, the earlier the bolting time was. The leaf age of overwinter of Qiyechangbai sown August 31 to September 14 was 2.1-3.1 leaves and the rate of returning green was 86.5%-92.1%, while the leaf age of overwinter of Hadacongl sown September 7 to September 14 was 2.3-2.7 leaves and the rate of returning green was 88.5%-93.8%, both varieties didn＇t bolt. In addition, in the same sowing time, the bolting rate of Hadacong I was higher than that of Qiyechangbai slightly.展开更多
Let {Xn} be a Markov chain with transition probability pij =： aj-（i-1）＋,i,j ≥ 0, where aj=0 providedj 〈 0, a0 〉 0, a0＋a1〈 1 and ∑∞n=0 an= 1. Let μ∑∞n=1nan. It is known that {Xn} is positive recurrent wh...Let {Xn} be a Markov chain with transition probability pij =： aj-（i-1）＋,i,j ≥ 0, where aj=0 providedj 〈 0, a0 〉 0, a0＋a1〈 1 and ∑∞n=0 an= 1. Let μ∑∞n=1nan. It is known that {Xn} is positive recurrent when μ 〈 1; is null recurrent when μ= 1; and is transient when μ 〉 1. In this paper, the integrability of the first returning time and the last exit time are discussed. Keywords Geom/G/1 queuing model, first returning time, last exit time, Markov chain展开更多
基金The author acknowledges the constructive discussion with Professors Mu-Fa Chen, Yong-Hua Mao, and Yutao Ma, and thanks the anonymous referees for their very valuable suggestions and careful reading of the draft, which greatly improved the quality of the paper. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11571043, 11771047, 11871008).
文摘An explicit and recursive representation is presented for moments of the first hitting times of birth-death processes on trees. Based on that, the criteria on ergodicity, strong ergodicity, and l-ergodicity of the processes as well as a necessary condition for exponential ergodicity are obtained.
基金Supported by Science and Technology Innovation Fund of Undergraduation of Northeast Agricultural University(20060201)
文摘Qiyechangbai and Hadacongl were used to study the relationship of the leaf age of overwinter to bolting and, returning green by the difference of sowing time. The results showed that the earlier the seeds were sown, the older leaf age of overwinter was, the higher the rates of returning green and bolting rate were, the earlier the bolting time was. The leaf age of overwinter of Qiyechangbai sown August 31 to September 14 was 2.1-3.1 leaves and the rate of returning green was 86.5%-92.1%, while the leaf age of overwinter of Hadacongl sown September 7 to September 14 was 2.3-2.7 leaves and the rate of returning green was 88.5%-93.8%, both varieties didn＇t bolt. In addition, in the same sowing time, the bolting rate of Hadacong I was higher than that of Qiyechangbai slightly.
基金Supported by National Natural Science Foundation of China(Grant Nos.11001070,11101113)Zhejiang Provincial Natural Science Foundation(Grant No.R6090034)
文摘Let {Xn} be a Markov chain with transition probability pij =： aj-（i-1）＋,i,j ≥ 0, where aj=0 providedj 〈 0, a0 〉 0, a0＋a1〈 1 and ∑∞n=0 an= 1. Let μ∑∞n=1nan. It is known that {Xn} is positive recurrent when μ 〈 1; is null recurrent when μ= 1; and is transient when μ 〉 1. In this paper, the integrability of the first returning time and the last exit time are discussed. Keywords Geom/G/1 queuing model, first returning time, last exit time, Markov chain
