In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While...
17 KB (2,564 words) - 19:12, 23 July 2024
Cramér's theorem is a fundamental result in the theory of large deviations, a subdiscipline of probability theory. It determines the rate function of a series...
2 KB (310 words) - 14:52, 23 May 2023
In mathematics, Laplace's principle is a basic theorem in large deviations theory which is similar to Varadhan's lemma. It gives an asymptotic expression...
3 KB (386 words) - 03:53, 13 March 2024
mathematics — specifically, in large deviations theory — the contraction principle is a theorem that states how a large deviation principle on one space "pushes...
2 KB (258 words) - 18:58, 9 June 2020
Rate function (redirect from Large deviation principle)
large deviations theory — a rate function is a function used to quantify the probabilities of rare events. Such functions are used to formulate large...
9 KB (1,305 words) - 18:08, 25 January 2024
Law of large numbers Law of the iterated logarithm Slutsky's theorem Delta method Asymptotic analysis Exact statistics Large deviations theory Höpfner...
9 KB (923 words) - 13:40, 23 February 2022
Rough path (redirect from Theory of rough paths)
the Contraction principle in large deviations theory reduces Freidlin–Wentzell's problem to demonstrating the large deviation principle for ( t , ε B t )...
29 KB (5,731 words) - 06:28, 12 July 2024
divergence Le Cam's theorem Large deviations theory Contraction principle (large deviations theory) Varadhan's lemma Tilted large deviation principle Rate function...
11 KB (1,000 words) - 14:07, 2 May 2024
Varadhan's lemma (category Large deviations theory)
In mathematics, Varadhan's lemma is a result from the large deviations theory named after S. R. Srinivasa Varadhan. The result gives information on the...
2 KB (318 words) - 13:17, 19 July 2023
In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts...
39 KB (6,409 words) - 11:54, 20 June 2024
specifically, in large deviations theory — the tilted large deviation principle is a result that allows one to generate a new large deviation principle from...
2 KB (247 words) - 00:12, 3 February 2024
Asymptotic equipartition property (category Information theory)
number of samples. Such results are studied in large deviations theory; intuitively, it is the large deviations that would violate equipartition, but these...
22 KB (3,951 words) - 06:42, 15 May 2024
In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion...
2 KB (171 words) - 03:23, 13 March 2024
Freidlin–Wentzell theorem (category Large deviations theory)
to Mark Freidlin and Alexander D. Wentzell) is a result in the large deviations theory of stochastic processes. Roughly speaking, the Freidlin–Wentzell...
3 KB (405 words) - 07:07, 10 May 2024
a German xDT format to transfer laboratory tests Large deviations theory, field of probability theory Learning Design and Technology, an academic program...
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has been suppressed by assuming that the variable has been measured as deviations from its mean) as X t = 1 ϕ ( B ) ε t . {\displaystyle X_{t}={\frac {1}{\phi...
35 KB (5,416 words) - 17:26, 7 July 2024
Fisher–Tippett–Gnedenko theorem Generalized extreme value distribution Large deviation theory Outlier Pareto distribution Pickands–Balkema–de Haan theorem Rare...
28 KB (2,729 words) - 08:26, 18 August 2024
Schilder's theorem (category Large deviations theory)
^{n}} to functional Wiener integration. The theorem is used in the large deviations theory of stochastic processes. Roughly speaking, out of Schilder's theorem...
6 KB (1,111 words) - 07:13, 10 May 2024
Sanov's theorem (category Information theory)
distribution. In the language of large deviations theory, Sanov's theorem identifies the rate function for large deviations of the empirical measure of a...
4 KB (731 words) - 11:02, 31 May 2024
standard deviations to either side of the mean, so that, with 95% probability the total range of values R represents four standard deviations so that s...
55 KB (7,609 words) - 17:48, 5 September 2024
{\displaystyle a} and b . {\displaystyle b.} This estimate is useful in large deviations theory under exponential moment conditions, because b ln b {\displaystyle...
13 KB (2,337 words) - 17:32, 22 April 2024
Freidlin–Wentzell theory, which is an important part of the large deviations theory. Freidlin and Wentzell are the authors of the first monograph on the large deviations...
7 KB (786 words) - 23:36, 26 January 2022
Dawson–Gärtner theorem (category Large deviations theory)
is a result in large deviations theory. Heuristically speaking, the Dawson–Gärtner theorem allows one to transport a large deviation principle on a “smaller”...
2 KB (256 words) - 21:15, 28 July 2024
Massachusetts Amherst in 1975. In 1984, he improved a key result in large deviations theory originally due to Jürgen Gärtner, which is now known as Gärtner-Ellis...
3 KB (228 words) - 19:27, 20 April 2024
implement in computer code, and lends itself well to risk management of large portfolios of options in real time. It is convenient to express the solution...
18 KB (2,483 words) - 22:26, 10 September 2024
distribution Laplace principle (large deviations theory) LaplacesDemon – software Large deviations theory Large deviations of Gaussian random functions LARS...
87 KB (8,280 words) - 14:50, 5 July 2024
the concept of Gromov–Hausdorff limits is closely related to large-deviations theory. Intrinsic flat distance David A. Edwards, "The Structure of Superspace"...
9 KB (993 words) - 19:21, 17 August 2024
Error exponents in hypothesis testing (category Large deviations theory)
tests are computed using Sanov's theorem and other results from large deviations theory. Consider a binary hypothesis testing problem in which observations...
5 KB (805 words) - 11:50, 15 June 2021
In probability theory and statistics, a continuous-time stochastic process, or a continuous-space-time stochastic process is a stochastic process for which...
2 KB (212 words) - 13:14, 20 June 2022
the deviations in real GNP are very small comparatively, and might be attributable to measurement errors rather than real deviations. We call large positive...
20 KB (2,699 words) - 17:45, 11 September 2024