Timo Seppäläinen delivered the Doob Lecture at the 45th Conference on Stochastic Processes and Their Applications (SPA) held in Ithaca, NY, on June 14-20, 2026. SPA is the main annual international conference on probability theory and its applications, organized by the Bernoulli Society for Mathematical Statistics and Probability. In addition to plenary lectures, each SPA features three keynote lectures named after Joseph Doob (1910-2004), Paul Lévy (1886-1971), and Oded Schramm (1961-2008). In the past Timo gave a plenary lecture at the 2010 SPA in Osaka and chaired the scientific program committee of the 2018 SPA in Gothenburg.