In the classic fairy tale, "The Emperor's New Clothes," Hans Christian Andersen uses the eyes of a child to challenge conventional wisdom and help others to see more clearly. In similar fashion, ...

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 ...

Brownian motion, the incessant random movement of microscopic particles driven by thermal fluctuations, plays a pivotal role in particle transport within porous media. Porous materials, characterised ...

Let Z(t) = (X(t), Y(t)), t ≥ 0, be the standard plane Brownian motion process. Let (R(t), θ1(t)) be the polar coordinates of Z(t). Suppose that $R(0) = r > 0$ with ...

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 ...