  Covariant stochastic partial differential equations are studied in any
dimension. A special class of such equations is selected and it is proven that
the solutions can be analytically continued to Minkowski space-time yielding
tempered Wightman distributions which are covariant, obey the locality axiom
and a weak form of the spectral axiom. Key words: stochastic partial
differential equations, white noise, covariant Markov generalized random
fields, Euclidean QFT, Schwinger functions, Wightman distributions
