Asymptotics of an Efficient Monte Carlo Estimation for the Transition Density of Diffusion Processes
Asymptotics of an Efficient Monte Carlo Estimation for the Transition Density of Diffusion Processes
复制标题
扩散过程转变密度的有效蒙特卡罗估计的渐进性
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Jun Yan
中科院分区：
文献类型：
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作者：
O. Stramer;Jun Yan
离散化模拟被广泛用于近似离散观测扩散的跃迁密度。最近提出的一种重要采样器，即改进布朗桥，因其相对于其他采样器的高效率而受到广泛关注。然而，对于这个采样器来说，在给定的计算资源下，如何平衡输入值的数量和蒙特卡罗模拟的数量之间的权衡是不清楚的。本文针对以改进布朗桥作为重要采样器的重要采样方法，提出了一种计算资源的渐近有效分配方法。通过研究欧拉离散化误差和蒙特卡罗误差两类误差，建立了最优权衡。通过两个仿真算例对主要结果进行了说明。
Discretized simulation is widely used to approximate the transition density of discretely observed diffusions. A recently proposed importance sampler, namely modified Brownian bridge, has gained much attention for its high efficiency relative to other samplers. It is unclear for this sampler, however, how to balance the trade-off between the number of imputed values and the number of Monte Carlo simulations under a given computing resource. This paper provides an asymptotically efficient allocation of computing resource to the importance sampling approach with a modified Brownian bridge as importance sampler. The optimal trade-off is established by investigating two types of errors: Euler discretization error and Monte Carlo error. The main results are illustrated with two simulated examples.