We consider a random walk ( Z (1) n , · · · , Z n ) ∈ Z with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a variance factor σ K = 2 K+2 with respect to the case of the classical simple random walk without constraint.

I discuss a novel technique for periodically extending by reflection an ordered series of phase-difference {xk.} to yield estimation of new frequency and time variances having improved longterm confidence and the same mean as the Allan variance. In addition, I describe a correction to a negative bias in the sample variance based on the actual number of observations in the measurements at long t...

Between-day variance is an ambiguous term representing either total variance or pure between-day variance. In either case, it is often incorrectly calculated even though analysis of variance (ANOVA) and other excellent methods of estimation are available. We used statistical theory to predict the magnitude of error expected from using several intuitive approaches to estimation of variance compo...

In this paper, we show how to exactly sample from the distribution of the maximum of a random walk with negative drift. We also explore related variance reduction methods.