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Titlebook: Gaussian Random Functions; M. A. Lifshits Book 1995 Springer Science+Business Media Dordrecht 1995 Gaussian distribution.Gaussian measure.

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11#
發(fā)表于 2025-3-24 03:23:49 | 只看該作者
Multi-Dimensional Gaussian Distributions,Distributions in ? .. We are now going to extend the notions introduced in Section 1 to the case when ? . is replaced by an arbitrary finite-dimensional Euclidean space ?..
12#
發(fā)表于 2025-3-24 08:08:34 | 只看該作者
13#
發(fā)表于 2025-3-24 11:50:32 | 只看該作者
14#
發(fā)表于 2025-3-24 15:55:27 | 只看該作者
15#
發(fā)表于 2025-3-24 20:22:43 | 只看該作者
Infinite-Dimensional Gaussian Distributions,.. For a numerical random variable ξ defined on a probability space (Ω,.,?), the basic probability characteristics: mean, variance, characteristic function, etc., can be easily calculated given the distribution of this random variable, that is a measure P defined on ?. by the formula ..
16#
發(fā)表于 2025-3-25 01:51:35 | 只看該作者
The Large Deviations Principle,Let {ξ ., . ∈ .} be a random function whose sample functions are bounded.
17#
發(fā)表于 2025-3-25 06:19:14 | 只看該作者
Exact Asymptotics of Large Deviations,Our consideration so far has been restricted to studying the . asymptotics of large deviations. We now focus on the methods which, in some cases, enable to find the . asymptotics.
18#
發(fā)表于 2025-3-25 08:27:49 | 只看該作者
Edward Blair,Kathleen Williamson ξ. If . ? ?., the term ‘.’ (or simply .) is used instead of the term ‘random function’; if . ? ?., . > 1, the expression ‘.’ is used. In these cases, the elements of . are interpreted as the time instants or space points, respectively. If . = ?, a random function ξ is called the ..
19#
發(fā)表于 2025-3-25 15:08:54 | 只看該作者
20#
發(fā)表于 2025-3-25 17:19:27 | 只看該作者
https://doi.org/10.1007/978-3-031-05789-2the kernel, some linear subspace .. ? .. Although this kernel has usually measure zero, it is very important for studying various properties of the measure. For instance, having shifted . by an arbitrary vector which belongs to .., we obtain a measure which is absolutely continuous with respect to .
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