Large deviations for rough path lifts of Watanabe's pullbacks of delta functions
Large deviations for rough path lifts of Watanabe's pullbacks of delta functions
复制标题
渡边 Delta 函数回调的粗略路径提升偏差较大
DOI：
10.1093/imrn/rnv349
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Yuzuru Inahama
中科院分区：
文献类型：
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作者：
三谷 健一; 斎藤 吉助; 高橋 泰嗣;Masahiko Taniguchi;Yuzuru Inahama
研究了与小参数强亚椭圆扩散过程相关的Donsker-Watanabe δ函数。它们是Wiener空间上的有限Borel测度，并允许粗糙路径提升。我们的主要结果是一个Schilder型的大偏差原理（LDP）的提升措施的几何粗糙路径空间的尺度参数趋于零。作为推论，我们得到了Takanobu和Watanabe证明的LDP，它是Freidlin-Wentzell型LDP的推广.
We study Donsker–Watanabe's delta functions associated with strongly hypoelliptic diffusion processes indexed by a small parameter. They are finite Borel measures on the Wiener space and admit a rough path lift. Our main result is a large deviation principle (LDP) of Schilder type for the lifted measures on the geometric rough path space as the scale parameter tends to zero. As a corollary, we obtain an LDP conjectured by Takanobu and Watanabe, which is a generalization of an LDP of Freidlin–Wentzell type for pinned diffusion processes.