Abstract:
A consistent test is constructed for the hypothesis that there is a particle which performs random walk along the integer lattice of the real line and carries a “useful signal” in the presence of “noise”. The limiting form of the linear approximation to the likelihood ratio is found to be a convolution of the standard normal distribution and a functional of the standard Wiener process.
Keywords:likelihood ratio statistics, random walk, signal detection in the presence of noise, functional of a Wiener process, problem of detection of random trajectories.