Concrete Functional Calculus

By R. Dudley, R. Norvaiša. 2010

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Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity (2018, background): “A typical example is the Brownian motion B, which has quadratic variation [B]2(t) = t along any refining sequence of partitions almost surely while at the same time having infinite 2-variation almost surely [11, 29]:”
Remarks on quantiles and distortion risk measures (2012, unknown): “Applying this formula to the distortion function defined in (5), we find that qg1⁄2X 1⁄4 F 1þ X ðpÞ: As FX(p) and FX(p) are in general not equal, we can indeed conclude that (6) is in general not valid for a l.”
Asymptotic theory of generalized estimating equations based on jack-knife pseudo-observations (2017, methodology): “The p-variation approach draws on results from Dudley and Norvaiša (1999, 2011) that treat basic functionals in p-variation that can be composed into the functionals we consider in examples.”
A Taylor expansion of the square root matrix function (2017, background): “For a more thorough discussion on higher Fréchet derivatives, we refer the reader to the seminal books of Cartan [11] and Dieudonné [14], as well as section 5.2 in the book by Dudley and Norvaisa [15] and the article by Higham and Relton [20].”