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I wonder if it is possible to define a Malliavin calculus w.r.t $G$-Brownian motion defined on a Sublinear Expectation Space available on this link. G–Brownian motion has a very rich and interesting new structure which nontrivially generalizes the classical one. Many interesting, attractive and challenging problems are also automatically provided within this new framework.

But Google does not provide any link on the Malliavin calculus in this new area.

Nevertheless all classical notions of stochastic calculus have been defined: Itô fomula, Girsanov theorem, white noise process, fractional Brownian motion etc..., except Malliavin calculus.

  1. What problems hinder this concept?
  2. Is for sublinearity of $G$-expectation which does not establish the integration by part formula? Any help is welcome. Thank's
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