On a multidimensional martingale with given conditional covariance structure

In this paper, a construction of an m-dimensional martingale with given conditional covariance structure is proposed. Application is given to certain stability problem of convergence rate in the martingale central limit theorem. Supported by the Lithuanian National Science Foundation and by the International Science Foundation (grant LI000). Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994.