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Friday, 2 November 2007

stochastic calculus - Moment Generating Function: Pulling a term out of k-times differentiation

In Wiersema: Brownian Motion Calculus on p. 205 (in an Annex on Moment Generating Functions (mgf)) the following equation is being presented dkoverdthetakleft(1overk!thetakmathbbE[Xk]right)=1overk!thetakdkoverdthetakmathbbE[Xk] with X being a random variable, theta the mgf-dummy variable and mathbbE the expectation operator (and k for the k'th moment of X).

My question: Why is it possible to pull the term 1overk!thetak out and in front of the k-times differentiation? Could anyone give me a hint or some intermediate steps? Or is this a typo? (Sorry if this is too elementary but I don't get it anyway - and I want to understand this!)

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