In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area) ${\cal A}(T)$ covered by the process ...

We give best tests and corresponding power functions for testing the hypothesis of no drift versus the alternative of positive linear drift in a one-dimensional Brownian motion process. The tests are ...

Stochastic processes have been applied to various areas of research to model systems that evolve probabilistically over time. By the 1930s, Brownian motion (i.e. the random movement of microscopic ...