Linear filtering problem for infinite-dimensional Gaussian processes is studied, the observation process being finite-dimensional. Integral equations for the filter and for covariance of the error are derived. General results are applied to linear SPDEs driven by Gauss–Volterra process observed at finitely many points of the domain.

中文翻译：

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希尔伯特空间中高斯过程的滤波

研究了无限维高斯过程的线性滤波问题，观测过程是有限维的。导出了滤波器和误差协方差的积分方程。一般结果适用于在域的有限多个点上观察到的由 Gauss-Volterra 过程驱动的线性 SPDE。