Zolota A. Properties of the random processes generated by the restriction of two-parameter fields in the plane.

The thesis is devoted to the problems of constructing of martingales by the means of restricting random field to the curve or to the collection of curves in the plane. The cases of restriction of stochastically continuous field with independ-ent increments to increasing and decreasing curves and re-striction of Wiener field to the finite number of increasing curves and piecewise monotonous curves are considered. A random process with independent increments, generated by the same s-algebra flow as mentioned restriction, is found in each particular case. The structure of martingales, adapted to the flow, is obtained as a sum of stochastic integrals. The examples of finding projection and calculating integral func-tion are given. The problem of "horizontal" and "vertical" signal filtration according to Wiener field observation on increasing field is solved.