On birth and death processes in symmetric random environment
On birth and death processes in symmetric random environment
复制标题
对称随机环境中的出生和死亡过程
DOI：
10.1007/bf01010495
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发表时间：
1984
影响因子：
1.6
通讯作者：
H. Kesten
中科院分区：
文献类型：
--
作者：
K. Kawazu;H. Kesten
本文证明了一维随机介质中过程的一个极限定理，它曾被认为是无序介质中跳跃传导的一个模型。在两个整数j和（j+ 1）之间的边上附加一个比率λj > 0。这些λj：j积分被视为独立的、同分布的随机变量，并代表介质。对于给定的值λj，X（t）是连续时间上的马氏链，它以相同的速率λj从j跳到（j + 1）和从（j + 1）跳到j.我们证明了在许多情况下存在正规化常数y（t）（它随t趋于0），使得X（t）/γ（t）的分布，或者更一般地说整个过程X（st）/γ（t）S <$0的分布，当t→ ∞时收敛到一个极限。极限过程是连续的、自相似的。
We prove a limit theorem for a process in a random one-dimensional medium, which has been considered before as a model for hopping conduction in a disordered medium. To the edge between the two integersj and (j+ 1) a rate λj > 0 is attached. Theseλj:j integral are taken as independent, identically distributed random variables, and represent the medium. For given values λj, X(t) is a Markov chain in continuous time which jumps fromj to (j + 1) and from (j + 1) toj at the same rate λj. We show that in many cases there exists normalizing constants y(t) (which tend to oo witht) such that the distribution of X(t)/γ(t), or more generally of the whole processX(st)/γ(t)S⩾0, converges to a limit as t→ ∞. The limit process is continuous and self-similar.