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.

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??

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

Of course, he's talking about Levy processes. Look at the norms, Banach space definitions, and exponential Polynomials.

<t>A thought for tomorrow:Under what conditions is there a linear map between a Hilbert space and a Banach space possible?A manifold in Banach space might be a surface such as the powder on a donut (torus). Banach space, bydefinition, does not have an inner product, but does have a norm. All RVs are...

On P.82:Bra, Ket inner product notation is used. This obviously applies to only Hilbert spaces; and incorrect forPoisson or Levy dists.

A Poisson norm is z= x + y and not z^2 = x^2 + y^2, therefore the Poission dist cannot be in Hilbert spaceand does not have an inner product (or at least not one that means anything).Got it?

<t>If you assume there is an inner product with obvious norm of z^2 = x^2 + y^2, then your RVs are assumedto be in Hilbert space, by definition. But if the RVs don't have Hilbert Space properties, then all you getare junk results. Only perfect Gaussian RVs are in Hilbert Space; almost all real world...

If there is an inner product, Levy (a<2) and Poission distributions are multivalued, ie two amplitudes.Do you see a little calibration problem??

Look...Anywhere there is an inner product or where the norm is z^2 = x^2 + y^2, the math is bogus.

Can't you read. Pick any page.

<t>thank you. So I was correct!Depends on what 'is' meansNow, perhaps you could give us precise line and page number references to the putative incorrectnesses in the aforementioned thesis.Doesn't the error run front to back.Also I am stilll waiting to find out where to download your thesis.If it we...

To explain further, C3:Voo Doo Math is mathematics that is so useless that even the spelling is incorrect.

In fact RVs don't even commute in most operations.

He uses all Hilbert space math even in maps to banach space. This give only correct answers forpure Gaussian Distributions.Levy (a<2) are not in Hilbert Space, neither are Poisson distributions. There is no inner product, nocovariance, etc.