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- W2314541244 abstract "The finite dimensional distributions of a stochastic process or (what is equivalent) their corresponding characteristic functions provide the basis from which more incisive information about the process is obtained. Instead of considering the whole family of finite dimensional characteristic functions, one can consider a single over-all characteristic function or characteristic functional of the process. The concept of characteristic functional was introduced for random additive set functions by Bochner [2, 3] and for point functions by LeCam [7]. It is the object of this paper to obtain inversion formulae for the characteristic functional of a process. For this purpose it seems convenient to define the characteristic functional in the following manner. Let {Ix, 0 < t ? 1} be a process of which almost all sample functions are in L, and vanish at the origin. Let {Pt, 0 ? t ? 1} be the Wiener process with almost all its sample functions also vanishing at the origin. We define the characteristic functional," @default.
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- W2314541244 date "1959-01-01" @default.
- W2314541244 modified "2023-10-17" @default.
- W2314541244 title "Inversion Formulae for Characteristic Functionals of Stochastic Processes" @default.
- W2314541244 cites W2008026092 @default.
- W2314541244 doi "https://doi.org/10.2307/1970091" @default.
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