integral representation theorem

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• Integral representation theorem for classical Wiener space — In mathematics, the integral representation theorem for classical Wiener space is a result in the fields of measure theory and stochastic analysis. Essentially, it shows how to decompose a function on classical Wiener space into the sum of its… …   Wikipedia

• Martingale representation theorem — In probability theory, the martingale representation theorem states that a random variable which is measurable with respect to the filtration generated by a Brownian motion can be written in terms of an Itô integral with respect to this Brownian… …   Wikipedia

• Clark-Ocone theorem — In mathematics, the Clark Ocone theorem (also known as the Clark Ocone Haussmann theorem or formula) is a theorem of stochastic analysis. It expresses the value of some function F defined on the classical Wiener space of continuous paths starting …   Wikipedia

• Clark–Ocone theorem — In mathematics, the Clark–Ocone theorem (also known as the Clark–Ocone–Haussmann theorem or formula) is a theorem of stochastic analysis. It expresses the value of some function F defined on the classical Wiener space of continuous paths starting …   Wikipedia

• Representation theory — This article is about the theory of representations of algebraic structures by linear transformations and matrices. For the more general notion of representations throughout mathematics, see representation (mathematics). Representation theory is… …   Wikipedia

• Integral transform — In mathematics, an integral transform is any transform T of the following form:: (Tf)(u) = int {t 1}^{t 2} K(t, u), f(t), dt.The input of this transform is a function f , and the output is another function Tf . An integral transform is a… …   Wikipedia

• Path integral formulation — This article is about a formulation of quantum mechanics. For integrals along a path, also known as line or contour integrals, see line integral. The path integral formulation of quantum mechanics is a description of quantum theory which… …   Wikipedia

• Logarithmic integral function — In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function. It occurs in problems of physics and has number theoretic significance, occurring in the prime number theorem as an estimate of the number of… …   Wikipedia

• Paley-Wiener integral — In mathematics, the Paley Wiener integral is a simple stochastic integral. When applied to classical Wiener space, it is less general than the Itō integral, but the two agree when they are both defined.The integral is named after its discoverers …   Wikipedia

• Mercer's theorem — In mathematics, specifically functional analysis, Mercer s theorem is a representation of a symmetric positive definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in (Mercer 1909), is one… …   Wikipedia

• Direct integral — In mathematics and functional analysis a direct integral is a generalization of the concept of direct sum. The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras. The concept was… …   Wikipedia