(adsbygoogle = window.adsbygoogle || []).push({}); Probability and Statistic on "Infinite-Dimensional" spaces

Hello..can the theories of Probability and Statistic be generalized to "Infinite-dimensional" spaces?..i mean if there are "probabilistic" phenomenon that include an infinite number of random variables, or include "random functions" instead of random numbers, or if you can define the probabilistic n-th "momentum" of a distribution in the sense of the functional integral:

[tex] \int D[\phi ]\phi^{n} P[\phi]= < \phi ^{n} > [/tex]

By the way..if Montecarlo integration does not depend on the dimensionality of space..:grumpy: why can't you perform infinite dimensional integrals...? simply in the form:

[tex] \int D[\phi ]\phi^{n} P[\phi]= \sum_{i} P[ \phi _i ] \phi_{i}^{n} + \sum_{r}a(r) \delta ^{r}\phi^{n} P[\phi] [/tex]

Or something similar...

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# Probability and Statistic on Infinite-Dimensional spaces

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