Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences (Q1346161)

Under appropriate conditions, the number of times that a stationary Gaussian process exceeds a fixed level has an approximately Poisson distribution. \textit{R. L. Smith} [ibid. 30, No. 2, 317-327 (1988; Zbl 0661.60033)] used the Stein-Chen method to quantify the error in this approximation. Here, the authors give a rather good general bound for the error, now considering a nonstationary Gaussian process satisfying Berman's condition, and a varying boundary. The proof is based on the Stein-Chen method and on the techniques of the first author [Z. Wahrscheinlichkeitstheorie Verw. Geb. 63, 257-270 (1983; Zbl 0494.60042)].