He obtained his PhD titled "Contribución al estudio de la integral estocástica" in 1975 at the University of Barcelona under the supervision of Francesc d'Assís Sales Vallès.
He received a Doctor Honoris Causa by the Université Blaise Pascal of Clermond-Ferrand in 1998.
He has been a Corresponding Member of the Real Academia de Ciencias Exactas Fisicas y Naturales of Madrid since 2003.
[1] In March 2011 the International Conference on Malliavin Calculus and Stochastic Analysis in honor of David Nualart took place at University of Kansas.
[4] He was named to the 2023 class of Fellows of the American Mathematical Society, "for contributions to Malliavin calculus, stochastic PDE's, and fractional Brownian motion".