Simple simulation of diffusion bridges with application to likelihood infer...

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英文文献：Simple simulation of diffusion bridges with application to likelihood inference for diffusions-扩散桥的简单模拟，并应用于扩散的似然推断
英文文献作者：Mogens Bladt,Michael S?rensen
英文文献摘要：
With a view to likelihood inference for discretely observed diffusion type models, we propose a simple method of simulating approximations to diffusion bridges. The method is applicable to all one-dimensional diffusion processes and has the advantage that simple simulation methods like the Euler scheme can be applied to bridge simulation. Another advantage over other bridge simulation methods is that the proposed method works well when the diffusion bridge is defined in a long interval because the computational complexity of the method is linear in the length of the interval. In a simulation study we investigate the accuracy and efficiency of the new method and compare it to exact simulation methods. In the study the method provides a very good approximation to the distribution of a diffusion bridge for bridges that are likely to occur in applications to likelihood inference. To illustrate the usefulness of the new method, we present an EM-algorithm for a discretely observed diffusion process. We demonstrate how this estimation method simplifies for exponential families of diffusions and very briefly consider Bayesian inference.

为了对离散观察扩散型模型进行似然推断，我们提出了一种模拟扩散桥的近似的简单方法。该方法适用于所有一维扩散过程，并具有欧拉格式等简单的模拟方法可应用于桥梁模拟的优点。与其他桥梁仿真方法相比，该方法的另一个优点是，当扩散桥在较长的时间间隔内定义时，该方法的计算复杂度在时间间隔的长度上呈线性关系。在仿真研究中，我们考察了新方法的准确性和效率，并与精确仿真方法进行了比较。在研究中，该方法为在似然推断应用中可能出现的扩散桥的分布提供了一个非常好的近似。为了说明新方法的有效性，我们提出了一个离散观测扩散过程的em算法。我们演示了这种估计方法如何简化指数扩散族，并非常简单地考虑贝叶斯推理。

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