Borell–TIS inequality
In mathematics and probability, the Borell–TIS inequality is a result bounding the probability of a deviation of the uniform norm of a centred Gaussian stochastic process above its expected value. The result is named for Christer Borell and its independent discoverers Boris Tsirelson, Ildar Ibragimov, and Vladimir Sudakov. The inequality has been described as “the single most important tool in the study of Gaussian processes.”Statement
Let be a topological space, and let be a centred Gaussian process on, with
almost surely finite, and let
Then and are both finite, and, for each,
