At the time of Davidson's birth, his parents lived in The Chantry, Thornbury, Gloucestershire.
His mother was Priscilla (née Chilver); his father, Brian Davidson, won a prize at Oxford for his study of classics, was president of the Oxford Union, and worked as a solicitor before becoming an executive with the Bristol Aeroplane Company.
[5] In stochastic analysis, also, Davidson has been described as a "remarkably original mathematician" who left a legacy of "tantalising unsolved problems".
[8] In 1975 a fund was established at Churchill College in his memory, endowed initially through the publication in his honour of two volumes[9] of papers, edited by E. F. Harding and D. G.
[10] A prize from the Rollo Davidson Trust Fund has been awarded annually since 1976 to early-career probabilists.