Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems
Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems
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DOI：
10.1016/j.spa.2011.07.005
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发表时间：
2011-11-01
影响因子：
1.4
通讯作者：
Ionides, Edward L.
中科院分区：
文献类型：
--
作者：
Breto, Carles;Ionides, Edward L.
对于马尔可夫计数过程，我们提出了一个无穷小离散指数。我们证明了，在标准矩存在条件下，一个过程是无穷(超)等离散的当且仅当它是简单(复合)的，即它以一个(或多个)单位(S)的跳跃递增，即使使用以前研究的指标，无穷小等离散过程可能是欠离散的、等离散的或过离散的。例如，当将连续时间白噪声引入简单过程的速率时，就会出现复合过程，从而导致Levy驱动的SDE。我们构造了多元无穷小超分散舱室模型和排队网络，适用于简单过程固有的矩约束不成立的应用。(C)2011爱思唯尔B.V.保留所有权利。
We propose an infinitesimal dispersion index for Markov counting processes. We show that, under standard moment existence conditions, a process is infinitesimally (over-)equi-dispersed if, and only if, it is simple (compound), i.e. it increases in jumps of one (or more) unit(s), even though infinitesimally equi-dispersed processes might be under-, equi- or over-dispersed using previously studied indices. Compound processes arise, for example, when introducing continuous-time white noise to the rates of simple processes resulting in Levy-driven SDEs. We construct multivariate infinitesimally over-dispersed compartment models and queuing networks, suitable for applications where moment constraints inherent to simple processes do not hold. (C) 2011 Elsevier B.V. All rights reserved.