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I'm looking for a reference to a book which develops an It\^{o} lemma for semi-martingales with values in infinite dimensional Hilbert-Manifolds. I expect the techniques to be the same but still I appreciate a reference as there are hints in some of the literature that these things are known.

So far I've only found finite dimensional stuff. Can any one point me in the right direction?

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    $\begingroup$ What did you mean by Hilbert-Manifold? $\endgroup$ – Zbigniew Feb 1 '17 at 21:58
  • $\begingroup$ I want to consider manifolds modeled on $\ell^2$ (or more generally on a sperable Hilbert space H). $\endgroup$ – AIM_BLB Feb 2 '17 at 2:35
  • $\begingroup$ "Introduction to stochastic analysis and Malliavin calculus" of Giuseppe Da Prato is a good introduction to stochastic analysis in Hilbert space. $\endgroup$ – Zbigniew Feb 3 '17 at 14:27
  • $\begingroup$ Hilbert manifolds not Hilbert vspace $\endgroup$ – AIM_BLB Feb 3 '17 at 16:08
  • $\begingroup$ But it may have a different cpnnectio $\endgroup$ – AIM_BLB Feb 6 '17 at 13:45
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As the question is general and observes the wide of the subject; I have chosen some reference.

Path Integrals on a Compact Manifold with Non-negative Curvature

Foundations of the Theory of Semilinear Stochastic Partial Differential Equations

Stochastic differential equations on manifolds

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  • $\begingroup$ I've found some results in Elworthy's stochastic analysis on manifolds but are there errata since nonthing in this vein seems to ever have been printed again? $\endgroup$ – AIM_BLB May 6 '17 at 0:28

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