A computation of the Littlewood exponent of stochastic processes
| Autor: | Ron C. Blei, J.-P. Kahane |
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| Rok vydání: | 1988 |
| Předmět: | |
| Zdroj: | Mathematical Proceedings of the Cambridge Philosophical Society. 103:367-370 |
| ISSN: | 1469-8064 0305-0041 |
| DOI: | 10.1017/s030500410006494x |
| Popis: | A stochastic process X = {X(t): t ∈ [0, 1]} on a probability space (Ω, , ℙ) is said to have finite expectation if the function defined on the measureable rectangles in Ω × [0, 1] byfor A ∈ and (s, t) ⊂ [0, 1] gives rise to a complex measure in each of its two coordinates (see [1], definition 1·1). Equivalently, X has finite expectation ifis finite. The function defined by (1), effectively a generalization of the Doléans measure (see e.g. [4] pp. 33–35), is extendible to a bona fide complex measure on Ω × [0, 1] if and only if its ‘total variation’ |
| Databáze: | OpenAIRE |
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