Short-Time Gibbsianness for Infinite-Dimensional Diffusions with Space-Time Interaction

Short-Time Gibbsianness for Infinite-Dimensional Diffusions with Space-Time Interaction
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时空相互作用的无限维扩散的短时吉布斯性

DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
W. Ruszel
W. Ruszel
中科院分区：
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文献类型：
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作者：
F. Redig;S. Rœlly;W. Ruszel

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We consider a class of infinite-dimensional diffusions where the interaction between the components has a finite extent both in space and time. We start the system from a Gibbs measure with a finite-range uniformly bounded interaction. Under suitable conditions on the drift, we prove that there exists t0>0 such that the distribution at time t≤t0 is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion of both the initial interaction and certain time-reversed Girsanov factors coming from the dynamics.