2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152397Covariant 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 distributions33 pages, LatexFunctional AnalysisMathematical PhysicsProbabilitytext