Conservative bounds in a certain first-passage-problem
Résumé
The goal is to calculate the probability that a discrete time autoregressive process (scalar or vector) leaves a given interval (domain) at least once during a certain period T. The distributions of the innovation process and the initial state are unknown but some special bounds for the cumulative distribution functions and/or for the probability density functions are available. Numerical methods to calculate the conservative bounds for the above-mentioned probability are considered. Such bounds can be useful in sequential change detection problem and also for risk estimation in some safety-critical applications.