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Calcul stochastique non adapté pour des processus à deux paramètres: Formules de changement de variables de type Stratonovitch et de type Skorohod. (Anticipative stochastic calculus for processes with two parameters: Change of variables formulae of Stratonovich and of Skorokhod type). (French) Zbl 0725.60053

We prove a Stratonovich-type change of variable formula for anticipative processes on \([0,1]^ 2\). The formula is the same as the existing one from deterministic calculus. In order to do so we define simple and double Stratonovich integrals. We deduce a Skorokhod-type change of variable formula which does not contain any line integral. Our method consists in using regularization of the Wiener process obtained by convolution.

MSC:

60H05 Stochastic integrals
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