Does anybody know a translation of Föllmer: Calcul d'Ito sans probabilités in English or German?
It seems to be a very interesting text - Abstract: "It is shown that if a deterministic continuous curve has a 'quadratic variation' in a suitable sense (which however depends explicitly on a nested sequence of time subdivisions, for example the standard dyadic one), then it satisfies a deterministic 'Ito formula' when composed with a twice differentiable function. Thus the only place where probability really appears in the derivation of Ito's formula is in the fact that, given any sequence of subdivisions, almost every path of a semimartingale admits a quadratic variation relative to this sequence (though no path may exist which has a quadratic variation relative to all sequences)"
See also: http://mathoverflow.net/questions/16664/convergence-and-non-convergence-of-left-point-and-mid-point-riemann-sums and first answer.
Other references along the same lines would also be appreciated - Thank you!