Probability theory
Runnenburg was appointed Lector in Probability theory and analysis at the University of Amsterdam in 1961. In 1962 he was promoted to Professor of Probability theory and analysis, and from 1966 to his retirement in 1997 was Professor of Pure and Applied Mathematics. Among his doctorate students were Gijsbert de Leve (1964), Laurens de Haan (1970), Fred Steutel (1971), Wim Vervaat (1972), August Balkema (1973), Frits Göbel (1974), Arie Hordijk (1974), Aegle Hoekstra (1983), Peter de Jong (1988) and Leo Klein Haneveld (1996).