Parametric estimation for planar random flights

The aim of this paper is to consider a parametric estimation problem for two-dimensional random motions at finite speed with an infinite number of directions (planar random flight). In particular we are interested in estimating the unknown value of the parameter λ, the underlying rate of the Poisson process, when the process is observed at n+1 equidistant discrete times. We introduce three different estimators, based on the distance between two consecutive observed points. Furthermore, their empirical performance is analyzed by means of a Monte Carlo analysis for small sample size n.