Exponential Integrability and Application to Stochastic Quantization

Abstract

We study the exponential integrability problem for I n (f n ), i.e., E exp{I n (f n )} < ∞, where I n (f n ) is a multiple Ito-Wiener integral on some Gaussian space arising from the constructive quantum field theory and from stochastic quantization. We also study a class of singular infinite-dimensional stochastic differential equations whose drift coefficients are measurable and unbounded. Using a condition due to Kazamaki, we prove the existence of a weak solution assuming some integrability conditions on the drift coefficient. Then we apply the exponential integrability theorem and the existence theorem to study infinite-dimensional stochastic differential equations of stochastic quantization.