AI 中文总结
本文针对空间参数泊松噪声泛函提出谱补偿方案，通过替换小振幅噪声提升误差界、降低计算复杂度，经数值实验验证了截断收敛速率的理论预测。
AI 中文摘要
本文计算由Lévy测度λ_β(u)du构建的Gel'fand三重空间中实现的泊松空间噪声泛函P′(u)，分离出三个离散化参数：小振幅截断、Donsker delta截断M和混沌阶N。对于稳定型强度λ_β(u)=cu^{-1-α}（0<α<2），用匹配的高斯空间噪声替代被丢弃的小振幅，将Wasserstein-1误差从O(ε^{1-α/2})提升至O(ε)，残差以O(ε^{α/2})渐近正态分布。该补偿将计算复杂度从O(τ^{-2α/(2-α)})降低至O(τ^{-α})。我们还评估了Gamma型边界（α=0）和指数回火，截断以代数速率（M）和超几何速率（N）收敛，所有预测的速率均通过Gil-Pelaez反演的确定性数值实验得到严格验证，消除了蒙特卡罗噪声。
英文摘要
This paper computes Poisson space noise functionals, $P^{\prime}(u)$, realised in a Gel'fand triple built from a Lévy measure $λ_β(u)du$. We isolate three discretisation parameters: a small-amplitude cut-off, a Donsker delta truncation M, and a chaos order N. For a stable-type intensity $λ_β(u)=cu^{-1-α}$ ($0<α<2$), replacing discarded small amplitudes with matched Gaussian space noise improves the Wasserstein-1 error from $O(ε^{1-α/2})$ to $O(ε)$. The residual is asymptotically normal at $O(ε^{α/2})$. This compensation reduces computational complexity from $O(τ^{-2α/(2-α)})$ to $O(τ^{-α})$. We also evaluate the Gamma-type boundary ($α=0$) and exponential tempering. Truncations converge algebraically (M) and super-geometrically (N). All predicted rates are tightly confirmed by deterministic numerical experiments via Gil-Pelaez inversion, eliminating Monte Carlo noise.
Comments24 pages, 7 figures. Submitted for publication
