Chaos hypothesis for a system interacting through shared resources
Chaos hypothesis for a system interacting through shared resources
复制标题
通过共享资源交互的系统的混沌假设
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
S. Méléard
中科院分区：
文献类型：
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作者：
C. Graham;S. Méléard
研究了一类纯跳跃多型相互作用系统的混沌假设。相互作用可能很强，没有对称性假设，系统不一定是马尔可夫的。我们使用相互作用图和耦合，并以精确的方式研究如何由一系列直接相互作用构成链式反应。我们得到了具有收敛速度的变分范数下的混沌假设，并由此导出了一般经验测度的收敛性。我们耦合的相互作用图的玻尔兹曼树，并表明，在每个上构建的过程之间的变化范数为零。这证明了当玻尔兹曼树收敛时，混沌以收敛速度的总变差传播。在轻对称性假设下，我们用一个非线性鞅问题刻画了该极限律。
SummaryWe study the chaos hypothesis for a wide class of pure-jump multitype interacting systems. The interaction may be strong, there is no symmetry assumption, and the system is not necessarily Markovian. We use interaction graphs and coupling and study in a precise way how a chain reaction is constituted by a series of direct interactions. We obtain the chaos hypothesis in variation norm with speed of convergence and deduce from it convergence of general empirical measures. We couple the interaction graph to a Boltzmann tree and show that the variation norm between the processes constructed on each goes to zero. This proves propagation of chaos in total variation with speed of convergence when the Boltzmann trees converge. Under light symmetry assumptions, we characterize the limit law by a nonlinear martingale problem.