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Results tagged with hilbert-spaces
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user 1004
A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.
23
votes
Gaussian processes, sample paths and associated Hilbert space.
No, it is not true for simple examples such as standard Brownian motion or a sequence of independent random variables.
Suppose $W$ is a standard Brownian motion on the interval $[0,T]$. The covarian …
- 17.1k
15
votes
Accepted
Can an operator have Exp(z) as its characteristic "polynomial"?
Here's a proof that $\exp(z)$ is not a characteristic function using the product expansion for the determinant, which is essentially equivalent to Lidskii's theorem stating that the trace of a trace c …
- 17.1k
10
votes
Does there exist an event independent of a given sigma-algebra?
No. If the probability space contains atoms then you can easily construct sub-$\sigma$-algebras which are not independent to any nontrivial events.
However, we can still construct examples, even for …
- 17.1k