2 problems

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Conjecture on Fisher information for SPDE observations without temporal differencing
Fisher-information conjecture. The bound above also holds for the Fisher information of $U_k$ itself, rather than only for the increment processes $\bar U_k$ .
Conjectureopenfisher-information spde statistical-inferencearXiv posted 2 days ago
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Conjecture on the minimax lower bound for SPDE parameter estimation with sparse spatial observations
Minimax lower-bound conjecture. The lower-bound conclusion stated for the regime $M/\sqrt N\gtrsim 1$ should also hold when $M/\sqrt N\to 0$ ; in particular, the minimax estimation…
Conjectureopenminimax-theory parameter-estimation spdearXiv posted 2 days ago

Conjecture on Fisher information for SPDE observations without temporal differencing