A method for B-spline filtration of data measured on a very precisely manufactured sphere is described in this paper. The method has been developed to decrease the uncertainty of measurement which can be obtained by least squares method commonly used when processing the measured data. The B-spline filtration is realised as a B-spline surface approximating the data measured on 3D coordinate measuring machine and transformed into the parametric space of the sphere. This transformaton eliminates the undesirable consequences of convex hull property of B-spline surfaces when processing convex data. Furthermore, the B-spline representation of the measured sphere can be considered as a certain replacement of the original sphere. Subsequently, the B-spline representation can be used for a new more precise measuring strategy in iterative measuring process. and Obsahuje seznam literatury
.In the paper D. Hoover, J. Keisler: Adapted probability distributions, Trans. Amer. Math. Soc. 286 (1984), 159–201 the notion of adapted distribution of two stochastic processes was introduced, which in a way represents the notion of equivalence of those processes. This very important property is hard to prove directly, so we continue the work of Keisler and Hoover in finding sufficient conditions for two stochastic processes to have the same adapted distribution. For this purpose we use the concept of causality between stochastic processes, which is based on Granger's definition of causality. Also, we provide applications of our results to solutions of some stochastic differential equations.