Large deviations for intersection measures of some Markov processes
Large deviations for intersection measures of some Markov processes
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DOI：
10.1002/mana.201800228
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发表时间：
2018-05
影响因子：
1
通讯作者：
T. Mori
中科院分区：
文献类型：
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作者：
T. Mori
考虑度量测度空间E中p个独立（可能不同）的m-对称Hunt过程到时间t的交测度Δ tIS，其Radon测度为m。当t→∞时，在t小于所有过程的生存时间的条件下，我们得到了E上有限测度集上的归一化交测度t-p ∈ tIS的Donsker-Varadhan型大偏差原理.这扩展了W. König和C. Mukherjee [16]，其中建立了p个独立的N维布朗运动在离开某个有界开集D <$RN之前的交测度的大偏差原理。我们还得到了对数矩母函数的渐近性态，它与X. Chen和J.罗森[7]关于独立布朗运动或稳定过程的交集测度。
Consider an intersection measure ℓtIS of p independent (possibly different) m‐symmetric Hunt processes up to time t in a metric measure space E with a Radon measure m. We derive a Donsker–Varadhan type large deviation principle for the normalized intersection measure t−pℓtIS on the set of finite measures on E as t→∞ , under the condition that t is smaller than life times of all processes. This extends earlier work by W. König and C. Mukherjee [16], in which the large deviation principle was established for the intersection measure of p independent N‐dimensional Brownian motions before exiting some bounded open set D⊂RN . We also obtain the asymptotic behavior of logarithmic moment generating function, which is related to the results of X. Chen and J. Rosen [7] on the intersection measure of independent Brownian motions or stable processes.