Abstract
A statistical manifold associated with a correlated walk (CW) model is examined by noticing a non-Riemannian curvature, called the α-curvature, as well as the Riemann curvature. Dynamical characteristics of the Riemann curvature and the α-curvature are discussed to have a close relation to the stability of the CW system. The statistical manifold is also found to be asymptotically flat in the meaning of the α (=1)-curvature, and also the jump probabilities characterizing the CW model is shown to have relation to a symmetry of the statistical manifold. Moreover a forecast is given about the statistical manifolds of n-step correlated-walk models and nonlinear models, and also such time-developing statistical manifolds are shown to be very analogous to the geometrical structure of Newton-Cartan theory of gravity.
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