The First Achievement of a Given Level by a Random Process
Sergei L. Semakov · IEEE Transactions on Information Theory · 2024
We propose a scheme for finding the probabilities of events related to crossings of a level by a random process. Using this scheme, we estimate the probability that the first achievement of a given level by the component$y_{1}(x)$of an n-dimensional continuous process${\mathbf { y}}(x)\!=\!\{y_{1}(x),\ldots,y_{n}(x)\}$occurs at some moment$x^{*}$from a given interval$(x',x'')$and, at this moment$x^{*}$, the other components$y_{2}(x^{*}),\ldots,y_{n}(x^{*})$satisfy given constraints. The need for estimating the above-mentioned probability arises, in particular, in the problems of ensuring the safety of an aircraft landing.