SPDE bridges with observation noise and their spatial approximation

Giulia di Nunno, Ortiz–Latorre, Salvador and Andreas Petersson

Stochastic Processes and their Applications, 2023, vol. 158, issue C, 170-207

Abstract: This paper introduces SPDE bridges with observation noise and contains an analysis of their spatially semidiscrete approximations. The SPDEs are considered in the form of mild solutions in an abstract Hilbert space framework suitable for parabolic equations. They are assumed to be linear with additive noise in the form of a cylindrical Wiener process. The observational noise is also cylindrical and SPDE bridges are formulated via conditional distributions of Gaussian random variables in Hilbert spaces. A general framework for the spatial discretization of these bridge processes is introduced. Explicit convergence rates are derived for a spectral and a finite element based method. It is shown that for sufficiently rough observation noise, the rates are essentially the same as those of the corresponding discretization of the original SPDE.

Keywords: Stochastic partial differential equations; Conditional distributions in Hilbert spaces; Finite element method; Spectral method; Stochastic reaction–diffusion equations (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:158:y:2023:i:c:p:170-207

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DOI: 10.1016/j.spa.2023.01.007

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