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平均穿越率为无穷的一类高斯过程AI 解读

Summary A stationary Gaussian process X(t) is defined as locally Markov if the slope of its autocorrelation function has a finite jump at the origin. For such a process the mean rate of crossings at an arbitrary level a is infinite. For small (t2 − t1), the probability that X(t1) − a and X(t2) − a have opposite signs is calculated, both with and without the auxiliary condition, X(t3)∈ (x3, x3+dx3], …, X(tn+2)∈(xn+2, xn+2+dxn+2], where the times t3,…, tn+2 are all outside…

平稳点过程的高阶性质AI 解读

SUMMARY This paper is concerned with joint distributions, joint moments, and joint renewal functions in a stationary point process. The random variables considered are (a) the numbers of events in adjacent intervals of given lengths, located either arbitrarily in time or by an arbitrary event, and (b) the lengths of intervals measured to the various events, beginning either at an arbitrary point or at an arbitrary event. The different bivariate probability functions are…