Demostratos Demostratianus was one of the four people (Aurelius Damas, Marcus Demostratianos, Demostratos Hegemonides, and Damianus - four sons of the famous athlete Marcus Aurelius Demostratos Damas, see Gouw (2009), no. 89) who erected a statue for Marcus Aurelius Demostratos Damas (see the inscription I.Sardis 79).
According to I.Sardis 79 ll. 18-22, emperors Septimius Severus and Caracalla decreed that the father's honorary functions as archiereus and xystarch were to be inherited by M. Aur. Demostratos Damas' sons.