Online Smoothing for Diffusion Processes Observed with Noise
Online Smoothing for Diffusion Processes Observed with Noise
复制标题
噪声观测扩散过程的在线平滑
DOI：
10.1080/10618600.2022.2027243
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发表时间：
2022
影响因子：
2.4
通讯作者：
Yonekura and Beskos
中科院分区：
文献类型：
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作者：
Tarao K;Daimon M;Son K;Nakanishi K;Nakao T;Suwazono Y;Isono S.;吉井智昭 多羅尾健太郎 孫慶淑 磯野史朗;森田 泰史 多羅尾 健太郎 孫 慶淑;Yonekura and Beskos
我们介绍了一种方法，用于在线估计一类可加泛函的平滑期望，在丰富的扩散过程族（可能包括跳跃）的背景下-在离散时间实例中观察到。我们通过处理增广路径空间克服了底层SDE转换密度的不可用性。例如，该方法可用于对指定类别的模型进行在线参数推理。在无限维路径空间上定义的算法在过去几年主要是在MCMC技术的背景下发展起来的。在那里，主要的好处是实现了在PC上使用的实际时间离散算法的无网格混合时间。我们自己的方法建立了无限维在线过滤的框架-一个重要的积极的实际结果是构建方差不随网格尺寸减小而增加的估计。除了正则性条件外，我们的方法原则上适用于弱假设，即SDE协方差矩阵是可逆的——相对于路径空间上定义的方法的MCMC或滤波文献中经常要求的限制性条件而言。
We introduce a methodology for online estimation of smoothing expectations for a class of additive functionals, in the context of a rich family of diffusion processes (that may include jumps) – observed at discrete-time instances. We overcome the unavailability of the transition density of the underlying SDE by working on the augmented pathspace. The new method can be applied, for instance, to carry out online parameter inference for the designated class of models. Algorithms defined on the infinite-dimensional pathspace have been developed the last years mainly in the context of MCMC techniques. There, the main benefit is the achievement of mesh-free mixing times for the practical time-discretised algorithm used on a PC. Our own methodology sets up the framework for infinite-dimensional online filtering – an important positive practical consequence is the construct of estimates with variance that does not increase with decreasing mesh-size. Besides regularity conditions, our method is, in principle, applicable under the weak assumption – relatively to restrictive conditions often required in the MCMC or filtering literature of methods defined on pathspace – that the SDE covariance matrix is invertible.