High Quality Content by WIKIPEDIA articles! In mathematics, the Paley–Wiener integral is a simple stochastic integral. When applied to classical Wiener space, it is less general than the It? integral, but the two agree when they are both defined.The integral is named after its discoverers, Raymond Paley and Norbert Wiener. Let i : H ? E be an abstract Wiener space with abstract Wiener measure ? on E. Let j : E? ? H be the adjoint of i. (We have abused notation slightly: strictly speaking, j : E? ? H?, but since H is a Hilbert space, it is isometrically isomorphic to its dual space H?, by the Riesz representation theorem.)It can be shown that j is an injective function and has dense image in H. Furthermore, it can be shown that every linear functional f ? E? is also square-integrable: in fact,

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