Laplace transforms and suprema of stochastic processes
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...The square root function can be expressed (Schürger 2002) as: √ x = 1 2 √ π ∫ ∞ 0 1 − e−sx s 3 2 ds (34) Taking expectations on both sides of (34) and interchanging the expectation and integral using Fubini’s theorem we get E( √ x) = 1 2 √ π ∫ ∞ 0 1 − E(e−sx) s 3 2 ds (35) The fair continuous…...
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...The square root function can be expressed (Schürger 2002) as: √ x = 1 2 √ π ∫ ∞...
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Cites methods from "Laplace transforms and suprema of s..."
...(A8) Schürger (2002) has shown that, after interchanging the expectation and integral using Fu- bini’s theorem, the expectation of the square root function can be expressed as, E[ √ x] = 1 2 √ π ∫ ∞ 0 1 − E[e−sx] s 3 2 ds. (A9) Using this identity, Formula (A8) can be simplified as: F(t, T,VIXt) =…...
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