A LAW OF LARGE NUMBERS FOR UPCROSSING MEASURES

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:53

Article

关键词: UPCROSSING MEASURE;    RAINFLOW COUNTING;    FATIGUE ANALYSIS;    STATIONARY PROCESS;    EXCURSION;    LAW OF LARGE NUMBERS;    RANDOM MEASURE;    VAGUE CONVERGENCE;   

DOI  :  10.1016/0304-4149(94)00002-6

来源: Elsevier

【 摘 要 】

We present a mathematical treatment of the so called RFC-counting which is applied to functions from subsets of R to R and which essentially counts upcrossings for each pair of levels. In mechanical engineering it is applied to stress or strain histories to assess their potential fatigue damage. We associate three measures on R(2) with RFC-counting and study their properties. Using the subadditive ergodic theorem of Kingman (1975) we prove a law of large numbers for these measures when they are applied to the paths of a stationary process. We compute the limit ($) over tilde mu explicitly e.g. for one-dimensional stationary diffusion processes. ($) over tilde mu may be compared with the spectral measure.

【 授权许可】

Free