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
Choose m numbers from the set {1,2,... ,n} at random without replacement. In this paper we first establish the limiting distribution of the longest length of consecutive integers and then apply the result to test rand...Choose m numbers from the set {1,2,... ,n} at random without replacement. In this paper we first establish the limiting distribution of the longest length of consecutive integers and then apply the result to test randomness of selecting numbers without replacement.展开更多
Transience and recurrence are among the most important concepts in Markov processes. In this paper, we study the transience and recurrence for right processes with a given weight function, and characterize them by pot...Transience and recurrence are among the most important concepts in Markov processes. In this paper, we study the transience and recurrence for right processes with a given weight function, and characterize them by potentials, excessive functions, first hitting times and last exit times of the process. We also study the properties of recurrent states.展开更多
In this article, we mainly discuss some potential theory in the framework of right Markov processes. We introduce the concept of α-excessive function, α-recurrence and α-transience for right processes with α ≤ 0,...In this article, we mainly discuss some potential theory in the framework of right Markov processes. We introduce the concept of α-excessive function, α-recurrence and α-transience for right processes with α ≤ 0, and give a thorough investigation.展开更多
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
基金The first author is supported by National Natural Science Foundation of China （Grant Nos. 10601047, 11001070） and Zhejiang Provincial Natural Science Foundation of China （Grant No. J20091364） the second author is partially supported by Hong Kong RGC CERG （Grant Nos. 602608 and 603710）
文摘Choose m numbers from the set {1,2,... ,n} at random without replacement. In this paper we first establish the limiting distribution of the longest length of consecutive integers and then apply the result to test randomness of selecting numbers without replacement.
文摘Transience and recurrence are among the most important concepts in Markov processes. In this paper, we study the transience and recurrence for right processes with a given weight function, and characterize them by potentials, excessive functions, first hitting times and last exit times of the process. We also study the properties of recurrent states.
文摘In this article, we mainly discuss some potential theory in the framework of right Markov processes. We introduce the concept of α-excessive function, α-recurrence and α-transience for right processes with α ≤ 0, and give a thorough investigation.
