This award was established to commemorate the achievements in the area of applied probability of Professor J. E. Moyal (1910-1998) who was a pioneer in the field of stochastic processes, particularly as applied in physics. He was a major contributor to the development of the theories of probabilistic quantum mechanics, Markov processes and population processes. The award, which is not given annually, is given in recognition of academic excellence in applied probability.

• 2020 – Sierra Pugh
• 2019 – Olivia Beck
• 2018 – Lei Yang and Lvou Zhang
• 2017 – Qian Xiong
• 2016 – Henry Scharf
• 2015 – Gabriel Young
• 2014 – Brook Russell
• 2013 – Grant Weller
• 2011 – Tingjin Chu
• 2008 – Stacey A. Hancock
• 2007 – Yu “Vicky” Yang
• 2004 – Gabriel Rodriguez-Yam
• 2003 – Beth Andrews
• 1999 – Philippe Naveau