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$p^{(t)}$ is a random variable, so perhaps we should have $\Omega = \{t \, , t \in [1, N] \, , \, \mathbb{E}(|p^{(t)}|^2)< \epsilon\}$ or something similar?
@TomCopeland Thank you very much for the advice, what is the Shannon-Nyquist sampling theorem used for? I apply it after using FFT to improve the accuracy?
@guest Thank you! I'm thinking of applying the Mill's ratio and approximate the integral by a lower and a upper bound. I hope these bounds approximate well the integral value.
