In mathematics and information theory, Sanov's theorem gives a bound on the probability of observing an atypical sequence of samples from a given probability...

function in Sanov's theorem. Convex conjugate – Generalization of the Legendre transformation Integral of inverse functions – Mathematical theorem, used in...

numbers (weak/strong) Law of the iterated logarithm Maximal ergodic theorem Sanov's theorem Zero–one laws (Blumenthal, Borel–Cantelli, Engelbert–Schmidt, Hewitt–Savage...

numbers (weak/strong) Law of the iterated logarithm Maximal ergodic theorem Sanov's theorem Zero–one laws (Blumenthal, Borel–Cantelli, Engelbert–Schmidt, Hewitt–Savage...

Kullback–Leibler divergence, the connection is established by Sanov's theorem (see Sanov and Novak, ch. 14.5). In a special case, large deviations are...

{\displaystyle X_{t}} is also a Gaussian process. In other cases, the central limit theorem indicates that X t {\displaystyle X_{t}} will be approximately normally...

numbers (weak/strong) Law of the iterated logarithm Maximal ergodic theorem Sanov's theorem Zero–one laws (Blumenthal, Borel–Cantelli, Engelbert–Schmidt, Hewitt–Savage...

uniformly distributed random phase. Where applicable, the central limit theorem dictates that at any point, the sum of these individual plane-wave contributions...

A_{\epsilon })} on each piece A ϵ {\displaystyle A_{\epsilon }} , we obtain Sanov's theorem, which states that lim n → ∞ 1 n ln ⁡ P r ( p ^ ∈ A ) = − inf p ^ ∈...

Error exponents for different hypothesis tests are computed using Sanov's theorem and other results from large deviations theory. Consider a binary hypothesis...

with Kobus Oosterhoff and Frits H. Ruymgaart, formulated and proved Sanov's theorem in a finer topology than had been known at the time. A paper he published...

can be extended to arbitrary f-divergences and other divergences. Sanov's theorem Cover, Thomas M.; Thomas, Joy A. (2006). Elements of Information Theory...

numbers (weak/strong) Law of the iterated logarithm Maximal ergodic theorem Sanov's theorem Zero–one laws (Blumenthal, Borel–Cantelli, Engelbert–Schmidt, Hewitt–Savage...

invertible n × n complex matrices was finite; he used this theorem to prove the Jordan–Schur theorem. Nevertheless, the general answer to the Burnside problem...

(notably an exponential family), it satisfies a generalized Pythagorean theorem (which applies to squared distances). Relative entropy is always a non-negative...

was proved by G. Nagy. The case n = pm holds by the Grishkov–Zelmanov Theorem. Conjecture: Let L be a finitely generated Moufang loop of exponent 4 or...