Timeline for What structure is needed to define a Gaussian distribution on a given space?
Current License: CC BY-SA 2.5
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| Mar 27, 2011 at 20:57 | comment | added | George Lowther | I think this is the correct generalization of normal distributions to the infinite dimensional setting. The process $X$ does not itslef lie in the Hilbert space though (see my old answer mathoverflow.net/questions/19020/brownian-motion-and-spheres/…). | |
| Mar 27, 2011 at 20:15 | comment | added | jzadeh | sorry is it appropriate to remove this as answer then? One last thing I can add is the construction of "brownian motion" in the free potability setting where you are working over von neumann algebras of operators as in section 1.1 of iecn.u-nancy.fr/~nourdin/4th-moment-Wigner-KNPS.pdf. Just in case you were unaware of an example of a type of Brownian motion taking values in a non commutative space. | |
| Mar 27, 2011 at 19:57 | comment | added | Simon Lyons | Thanks for your comment. The construction in Nualart that you mentioned is for a set of one-dimensional Gaussians indexed by a Hilbert space. I'm really looking for analogues of the normal distribution that take values in a space $S$. | |
| Mar 27, 2011 at 19:26 | history | edited | jzadeh | CC BY-SA 2.5 |
added 74 characters in body
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| Mar 27, 2011 at 19:08 | history | answered | jzadeh | CC BY-SA 2.5 |