Density Estimation of Lévy Measures for Discretely Observed Diffusion Processes with Jumps
Density Estimation of Lévy Measures for Discretely Observed Diffusion Processes with Jumps
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离散观测跳跃扩散过程的 Lévy 测度的密度估计
DOI：
10.14490/jjss.36.37
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Y. Shimizu
中科院分区：
文献类型：
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作者：
Y. Shimizu
从一些离散的观测数据出发，研究了多维跳跃-扩散模型Levy测度的非参数估计。我们假设跳跃项是由一个Levy测度有限的Levy过程驱动的，即复合泊松过程。在终端时间趋近于无穷大，同时观测值间距离趋近于零的采样方案下，构造了Levy密度的核估计量，并给出了l2 -一致性和MSE意义上的最优速率。首先，我们考虑连续给出观测值的情况，然后将其与离散观测值的情况进行比较。
We study a nonparametric estimation of Levy measures for multidimensional jump-diffusion models from some discrete observations. We suppose that the jump term is driven by a Levy process with finite Levy measure, that is, a compound Poisson process. We construct a kernel-estimator of the Levy density under a sam- pling scheme where the terminal time tends to infinity and at the same time the distance between the observations tends to zero fast enough, and show the L 2 - consistency and the optimal rate in the MSE sense. First, we consider the case where the observations are given continuously and then compare it to the discretely observed case.
在完全错误指定的模型下离散观察到的遍历扩散的估计
DOI：
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发表时间：
2008
期刊：
影响因子：
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作者：
Uchida;M.
通讯作者：
M.