While consistency of the maximum likelihood estimator of the drift matrix in a multi-dimensional continuous time Ornstein-Uhlenbeck process holds under rather general conditions, little is known about the rate of convergence and the limiting distribution of the estimator when the underlying process is not ergodic. The objective of the paper is to investigate these questions for an important exa...

This note is a study of the Ornstein-Uhlenbeck bridge and its main properties. We present the derivation of its canonical decomposition in the first section of the paper using filtration enlargement techniques. In the second section, we present its Karhunen-Loève expansion, for any value of the initial variance and mean-reversion parameter (or mean-repulsion if negative). In the third section, ...

Also, a process {Yt : t ≥ 0} is said to have independent increments if, for all t0 < t1 < . . . < tn, the n random variables Yt1 − Yt0 , Yt2 − Yt1 , ..., Ytn − Ytn−1 are independent. This condition implies that {Yt : t ≥ 0} is Markovian, but not conversely. The increments are further said to be stationary if, for any t > s and h > 0, the distribution of Yt+h− Ys+h is the same as the distributio...

Sediment tracers are increasingly employed to estimate bed load transport and landscape evolution rates. Tracer trajectories are dominated by periods of immobility (“waiting times”) as they are buried and reexcavated in the stochastically evolving river bed. Here we model bed evolution as a random walk with mean-reverting tendency (Ornstein-Uhlenbeck process) originating from the restoring effe...

We consider a positive stationary generalized Ornstein-Uhlenbeck process