Data assimilation algorithm for stochastic evolution equations based on discrete-time observation

doi:10.1016/j.camwa.2026.05.015

Data assimilation algorithm for stochastic evolution equations based on discrete-time observation

2026-05-28

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DOI：10.1016/j.camwa.2026.05.015

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This paper is concerned with the data assimilation of stochastic evolution equations based on discrete-time observation. For stochastic ordinary differential equations, a new data assimilation algorithm is introduced. Our main results show that the approximating solution, obtained by our algorithm, converges to the unknown reference solution over time almost surely. For stochastic Chafee-Infante reaction-diffusion equations, a continuous data assimilation algorithm is given based on ideas that have been developed for designing finite dimensional feedback controls. Some numerical examples are given to verify our results.

Keywords:

data assimilation

stochastic evolution equations

discrete-time observation

stochastic ordinary differential equations

stochastic Chafee-Infante reaction-diffusion equations

Data assimilation algorithm for stochastic evolution equations based on discrete-time observation

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