Since stochastic analysis in infinitely dimensional spaces has been developed in the past decades, e.g. Hida distributions, Malliavin calculus, just to name a few. However, I have almost never seen that the models from forementioned fields have been treated from a statistician's perspective. To be precise, I mean here, as a statistician, his interest would be recovering the parameter of the model to which the observations are made, (knowns as inference, parameter identification, calibration, etc).

My questions can be summarized as follows.

  1. Do there exist any statistical researches on inference of processes (or SDEs), using the techniques established in forementioned fields, namely different from (semi-)martingale approach? If so, could one suggest any references on the subject?

  2. (side question) Why Malliavin calculus seems (much) more popular than Hida's distribution?


(1) Malliavin calculus has been used in mathematical finance to compute sensitivity parameters of option prices, see these lecture notes and this research article. And Statistical inference and Malliavin calculus is a more general application of Malliavin calculus to statistics.

(2) Hida's white-noise infinite dimensional calculus relies on built-in spaces of stochastic distributions (Hida and Kondratiev spaces). The Malliavin calculus is more flexible, in that it allows one to build solution spaces optimal for the equation at hand. In A Stochastic Modeling Methodology Based on Weighted Wiener Chaos and Malliavin Calculus this feature of Malliavin calculus was used to obtain more powerful numerical approximation schemes than would follow from Hida distributions.


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