The dynamics of sensors operated devices such as Automated Mobile Robots and more generally automated target seeking devices is studied in presence of noise. We introduce a simple and analytically tractable class of dynamics which permits to classify qualitatively and somehow quantitatively also the approach to the targets when fluctuations corrupt the ideal trajectories. Our model constitute a first evaluation of the feasibility of an efficient approach when the parameters of the model (statistics of the noise, lengths of the path and progressing steps and heading velocity) are known.

In this article we consider local solutions for stochastic Navier Stokesequations, based on the approach of Von Wahl, for the deterministic case. Wepresent several approaches of the concept, depending on the smoothnessavailable. When smoothness is available, we can in someway reduce thestochastic equation to a deterministic one with a random parameter. In thegeneral case, we mimic the concept of local solution for stochasticdifferential equations.

We consider maximum likelihood estimators for parameters of diffusion processes that are generated by nth-order Ito equations. We establish asymptotic consistency as well as convergence in distribution to normality for the estimators. Examples are presented and discussed.