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Lévy process
A Lévy process is a stochastic process with stationary, independent increments and càdlàg paths, combining continuous motion with abrupt jumps and generalizing Brownian motion and the Poisson process.
Lévy–Khintchine formula and Lévy–Itô decomposition
The Lévy–Khintchine formula and Lévy–Itô decomposition characterize Lévy processes: the formula encodes the distribution in a drift, Gaussian, and jump triplet, while the decomposition builds the process from those parts.
Lexicographic order
Lexicographic order, also called lexical or dictionary order, is a way of ordering sequences by comparing them position by position, deciding at the first position where they differ.
LF (logical framework)
LF, short for the Edinburgh Logical Framework, is a typed lambda-calculus with dependent types designed as a meta-language for defining logics, presented by Harper, Honsell, and Plotkin in 1987.
Liar paradox
The Liar paradox, also known as Eubulides' paradox, is the semantic paradox of a sentence like "This sentence is not true" that seems both true and false.
Liber Abaci
Liber Abaci, also spelled Liber Abbaci, is a 1202 Latin treatise by Leonardo Pisano, known as Fibonacci, that taught calculation with Hindu-Arabic numerals and posed the rabbit problem behind the Fibonacci sequence.
Lie algebra
A Lie algebra is a vector space with a bilinear, antisymmetric Lie bracket satisfying the Jacobi identity, recording the infinitesimal behavior of continuous symmetry groups, named after Sophus Lie.
Lie algebra cohomology
Lie algebra cohomology, also called cohomology of Lie algebras, is a cohomology theory for Lie algebras introduced by Élie Cartan in 1929, computed via the Chevalley–Eilenberg complex.
Lie algebra extension
A Lie algebra extension is a Lie algebra fitting a short exact sequence, with splitting, central extensions, and classification by Lie algebra cohomology, founded by Chevalley and Eilenberg in 1948.
Lie algebra representation
A Lie algebra representation is a way of realizing a Lie algebra as linear operators on a vector space, via a bracket-preserving homomorphism into endomorphisms.
Lie bialgebra
A Lie bialgebra, or Poisson-Hopf algebra, is a Lie algebra with a compatible cobracket, introduced by Vladimir Drinfeld in 1983 as the structure underlying Poisson-Lie groups.
Lie derivative
The Lie derivative is an operator on a differentiable manifold that measures the rate of change of a tensor field along the flow of a vector field.
Lie group
A Lie group is a set carrying compatible structures of a group and a smooth manifold, named for Sophus Lie and central to continuous symmetry in mathematics and physics.
Lie group analysis
Lie group analysis is a mathematical method that finds and exploits continuous symmetry groups of differential equations to produce similarity solutions, reduce order or variables, and derive conservation laws.
Lie superalgebra
A Lie superalgebra is a ℤ₂-graded algebra with even and odd parts whose bracket obeys graded symmetry and Jacobi identities, generalizing a Lie algebra and underlying supersymmetry in physics.
Lie symmetry analysis
Lie symmetry analysis is a mathematical method that finds continuous transformation groups leaving a differential equation invariant, then uses those symmetries to construct exact solutions and reduce the order of equations.
Lies, damned lies, and statistics
"Lies, damned lies, and statistics" is a phrase describing the persuasive power of statistics to bolster weak arguments, popularized by Mark Twain, who credited Disraeli in 1907.
Life table
A life table, also called a mortality table or actuarial table, is a statistical table describing a population's mortality by age, showing death probabilities, survivors, and remaining life expectancy.
Lifting scheme
The lifting scheme is a method for constructing wavelets and computing the discrete wavelet transform through split, predict, and update steps, introduced by Wim Sweldens in 1995.
Likelihood function
The likelihood function describes how probable the observed data are under each candidate parameter value of a statistical model, and is central to maximum likelihood estimation and Bayesian inference.
Likelihood principle
The likelihood principle is a principle of statistical inference stating that the likelihood function fully captures the evidence in experimental data, independent of the experimental design.
Likelihood ratios in diagnostic testing
Likelihood ratios in diagnostic testing: LR+ = sensitivity/(1−specificity), LR− = (1−sensitivity)/specificity; they convert pretest odds to posttest odds via Bayes' theorem, are prevalence-independent, and guide rule-in and rule-out decisions.
Likelihood-free inference (statistics)
Likelihood-free inference is a family of simulation-based statistical methods, including approximate Bayesian computation (ABC), that estimate posterior distributions for models whose likelihood is intractable but whose data can be simulated.
Likelihood-ratio test
The likelihood-ratio test, also known as the LR test, is a statistical test comparing two nested models fitted by maximum likelihood, introduced by Neyman and Pearson in 1928.
Limaçon
The limaçon, also called Pascal's snail, is a plane algebraic curve of order 4, the conchoid of a circle taken with respect to a point on its circumference.
Limit (category theory)
In category theory, a limit of a diagram is a universal cone that every other cone factors through uniquely, generalizing products, equalizers, pullbacks, and terminal objects; it was named by Daniel Kan in 1958.
Limit (mathematics)
In mathematics, a limit is the value a function or sequence approaches as its input approaches some value, the foundational concept underlying continuity, derivatives, integrals, and convergence.
Limit cycle
A limit cycle is an isolated closed trajectory in the phase space of a differential equation, a periodic solution that nearby trajectories spiral toward or away from.
Limit of a function
The limit of a function is the value its output approaches as its input approaches a given point, and it underlies continuity, derivatives, and integrals in calculus.
Limit of a sequence
The limit of a sequence is the number its terms approach and stay near; a sequence with such a number is called convergent, one without, divergent.