On statistical manifolds of solutions of martingale problems

We consider geometrically regular statistical models defined by local densities of probability measures corresponding to discrete or continuous time Markov processes and smoothly depending on a finite dimensional parameter. Evolution equations are derived in terms of the generators of the underlying Markov additive processes for the elements of the related Fisher information matrix and the skewness tensor defining the Riemannian metric and the Amari-Chentsov's affine α-connections as functions of time and starting points of Markov processes. Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikes Rinkinys, Vol. 35, No. 4, pp. 456–468, October–December, 1995.