H ? C 1 Maps and Elliptic Spdes with Non-linear Local Perturbations of Nelson's Euclidean Free Eld
نویسندگان
چکیده
Elliptic stochastic partial diierential equations (SPDE) with polynomial perturbation terms deened in terms of Nelson's Euclidean free eld on R d are studied using results by S. Kusuoka and A.S. Ust unel and M. Zakai concerning transformation of measures on abstract Wiener space. SPDEs of this type arise, in particular, in (Euclidean) quantum eld theory with interactions of the polynomial type. The probability laws of the solutions of such SPDEs are given by Girsanov probability measures, that are non-linearly transformed measures of the probability law of Nelson's free eld deened on subspaces of Schwartz space of tempered distributions.
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