http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Speed of random walk and resistance
Konsowa, Mokhtar,Oraby, Tamer 한국통계학회 2012 Journal of the Korean Statistical Society Vol.41 No.4
We give a simple formula to calculate the speed of weighted random walks on nonnegative integers and on spherically symmetric trees.
SITE-DEPENDENT IRREGULAR RANDOM WALK ON NONNEGATIVE INTEGERS
Konsowa, Mokhtar-H.,Okasha, Hassan-M. The Korean Statistical Society 2003 Journal of the Korean Statistical Society Vol.32 No.4
We consider a particle walking on the nonnegative integers and each unit of time it makes, given it is at site k, either a jump of size m distance units to the right with probability $p_{k}$ or it goes back (falls down) to its starting point 0, a retaining barrier, with probability $v_{k}\;=\;1\;-\;p_{k}$. This is a Markov chain on the integers $mZ^{+}$. We show that if $v_{k}$ has a nonzero limit, then the Markov chain is positive recurrent. However, if $v_{k}$ speeds to 0, then we may get transient Markov chain. A critical speeding rate to zero is identified to get transience, null recurrence, and positive recurrence. Another type of random walk on $Z^{+}$ is considered in which a particle moves m distance units to the right or 1 distance unit to left with probabilities $p_{k}\;and\;q_{k}\;=\;1\;-\;p_{k}$, respectively. A necessary condition to having a stationary distribution and positive recurrence is obtained.
Speed of random walk and resistance
Mokhtar Konsowa,Tamer Oraby 한국통계학회 2012 Journal of the Korean Statistical Society Vol.41 No.4
We give a simple formula to calculate the speed of weighted random walks on nonnegative integers and on spherically symmetric trees.
Irregular Random Walk on Nonnegative Integers
Mokhtar H. Konsowa... et al KYUNGPOOK UNIVERSITY 2000 Kyungpook mathematical journal Vol.40 No.2
Consider a walker that makes a jump of size m distance units to the right with probability p and n distance units to the left with probability 1-p. The state space is considered to be the nonnegative integers and the state 0 is a retaining barrier. If the walker is at a distance less than or equal to n from 0, the jump to the left will be to the state 0. We call this Markov chain irregular random walk (IRW). The type of the IRW of being transient, null recurrent, or positive recurrent is determined in terms of m,n and p. A state-dependent IRWis also considered.