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In mathematics, Young's inequality for products is a mathematical inequality about the product of two numbers. [1] The inequality is named after William Henry Young and should not be confused with Young's convolution inequality. Young's inequality for products can be used to prove Hölder's inequality. It is also widely used to estimate the ...
A sample path of compound Poisson risk process. The theoretical foundation of ruin theory, known as the Cramér–Lundberg model (or classical compound-Poisson risk model, classical risk process [2] or Poisson risk process) was introduced in 1903 by the Swedish actuary Filip Lundberg. [3] Lundberg's work was republished in the 1930s by Harald ...
The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) [1][2][3][4] is an upper bound on the inner product between two vectors in an inner product space in terms of the product of the vector norms. It is considered one of the most important and widely used inequalities in mathematics.
Cantelli's inequality. In probability theory, Cantelli's inequality (also called the Chebyshev-Cantelli inequality and the one-sided Chebyshev inequality) is an improved version of Chebyshev's inequality for one-sided tail bounds. [1][2][3] The inequality states that, for. where. Applying the Cantelli inequality to gives a bound on the lower tail,
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. [1] It is used most often to compare two numbers on the number line by their size. The main types of inequality are less than (<) and greater than (>).
Convolution is a mathematical operation involving the addition of each element of an image to its immediate neighbors, weighted by kernel elements.
Rearrangement inequality. In mathematics, the rearrangement inequality[1] states that for every choice of real numbers and every permutation of the numbers we have. Informally, this means that in these types of sums, the largest sum is achieved by pairing large values with large values, and the smallest sum is achieved by pairing small values ...
Poincaré inequality. In mathematics, the Poincaré inequality[1] is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. The inequality allows one to obtain bounds on a function using bounds on its derivatives and the geometry of its domain of definition. Such bounds are of great importance in the ...