Nonlinear martingale theory for processes with values in metric spaces of nonpositive curvature

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Convergence rates for the generalized Fréchet mean via the quadruple inequality (2018, background): “some extend. [Stu03] shows how some important theorems of probability theory in Euclidean spaces, like the law of large numbers and Jensen’s inequality, translate to non-Euclidean Hadamard spaces. In [Stu02] martingale theory on Hadamard spaces is discussed. Turning to more applied topics, [Baˇc14b]”
Geometry of the Space of Phylogenetic Trees (2001, background): “A clear account of this type of mean value and its properties can be found in [40, 41].”
A Semigroup Approach to Harmonic Maps (2005, background): “i=1 Xi(w) to γ1 := Xn(w). See Sturm [ 52 ]. Examples of spaces with globally nonpositive curvature in the sense of A.D.”