Summary
We give a general construction of infinite dimensional Ornstein-Uhlenbeck processes. We present expansions of these processes based on the expansion of the covariance operators in generalized eigenfunctions, and we answer positively some question left open by J.B. Walsh on properties of the hitting times of these processes.
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Partially supported by NSF-Grant MCS 8202045
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Antoniadis, A., Carmona, R. Eigenfunction expansions for infinite dimensional Ornstein-Uhlenbeck processes. Probab. Th. Rel. Fields 74, 31–54 (1987). https://doi.org/10.1007/BF01845638
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DOI: https://doi.org/10.1007/BF01845638