Look the top of page 6. This a map from all non-Gaussian distributions to Gaussian ones.

I have not read the thesis but I have looked at the joint papers with Teichmann and I think the confusion is as follows. They start with a Hilbert space H of forward curves, but they can't prove any theorems about H because the operator d/dx is unbounded. So they define a certain subset D of H, equipped with a sequence of seminorms (defined in terms of the original norm induced by the inner product on H) that make D into a Frechet space on which d/dx is a bounded linear operator; and D has certain other nice properties that make it possible for them to prove the Frobenius theorem they need. D does not simply inherit the Hilbert space structure from H. That confused me initially; it took me a long time to understand what they were getting at.

I looked up the thesis, and it looks just fine -- whether that's an academic exercise or not is beside the point. If it contains errors, they are certainly nothing as simple minded as what's being raised here. The author states his assumptions, and his results are very correct within these assumptions.

I just looked at page 6 : it's just definitions. My feelings on this thread are1) newton started by saying the thesis was "voodoo math"2) he has failed to substantiate this claim in anyway3) we now have a shift to the statement that it's not useful rather than wrong4) Newton's anonymous statements in this thread are arguably libellous and under English law, this means that Paul could be sued successfully for libel5) this sort of thread only detracts from the usefulness of the forums here6) I intend to ignore all of Newton's posts and threads in future and I would ask all other serious researchers on this forum to do likewise. 7) I would like to know why Newton is so shy about letting us see some of his own research. MJ

mj,Don't worry. there's one other property a Hilbert Space has that a Banach space doesn't. That is, RV's inHilbert Space (Gaussian) can be independent. RVs in Banach Space are never independent.Does the math you checked still work??

mj,So how can a stochastic process with correlated noise, be mapped to one with BM? The thesis didnot handle the correlation. This is the problem with the math of Hilbert space.

Quote 4) Newton's anonymous statements in this thread are arguably libellous and under English law, this means that Paul could be sued successfully for libel5) this sort of thread only detracts from the usefulness of the forums here I fully agree. The whole thing is not only in bad taste, but also borders on libel. The forum is frequented by a very large number of professionals. You cannot have a participant throwing statements like those made below, with names and affiliations, and supports them with lots of circular, vacuous arguments. Someone who casually scans the thread may actually get the impression that there is a serious discussion about the allegations being made, and that there may actually be any truth in them.