Prediction of confidence limits for the probability of nonexceedance of an admissible level by a stochastic process (Q1116604)

A considerable interest is attached in applications to the estimation and prediction of the probability of nonexit of a stochastic process from the admittance field in the statistical approach, i.e., based on information obtained from trials on a small number of (small sample). In this setting the blow-out problem for stochastic processes has been practically never considered. We investigate in the statistical setting the blow-out problem for two types of stochastic processes: stationary (with a high admittance level), and so-called semistochastic, i.e., processes representable by their canonical decomposition. To estimate the parameters of rejection models that characterize these two types of stochastic processes, we use indirect (rather than direct, which is often tedious) measurements on their realizations which permit us to determine the fraction of realizations that exceed an admissible level (or a ``more severe'' level) at separate moments of time.