Re: Hilbert spaces in stochastics

From: Stephen Miller (anon_at_talkincity.com)
Date: 06/16/04 

Date: Wed, 16 Jun 2004 13:30:02 +0000 (UTC)

On 11 Jun 2004 13:09:37 -0500, Herman Rubin wrote:
>In article <llgn0e3ao53y@legacy>, Stephen Miller
<anon@talkincity.com> wrote:
>>On 10 Jun 04 16:10:32 -0400 (EDT), neale wrote:
>
>
>>>Are there applications of Hilbert spaces in the analysis of
>>stochastic
>>>processes? What would be some examples?
>
>
>>I don't know if this is a facile comment, but given a finite number
of
>>random variables the covariance matrix can be used to construct an
>>inner product on the space of linear combinations of the variables.
>>This could I'm sure be extended to infinite dimensional spaces.
>>Whether or not anyone does it is a different matter
>
>This is used, as are other aspects of Hilbert spaces.
>The Karhunen-Loeve representation is a specific use
>of this for processes. Reproducing kernel Hilbert
>spaces have been used to analyze some processes, and
>a one time this was a hot topic.
>

As it happens I am doing some personal "research" at the moment which
uses these ideas (on a basic level). Can you recommend a decent book
or set of notes?

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