Neither Runciman nor Nicol (whom I just looked up) mention any external influences on the Hesychast movement. In view of the long standing line of Christian ascetic and introspective mystics, who in the early centuries of Christianity had initiated the monastic tradition, I think it was probably autonomous.
As the Wikipedia article says, the parallels with Eastern religions are rather superficial, hesychast practises are somewhat generic to religions, like sacrifices and prayers etc, and can be found everywhere.
Interesting and characteristic though, that the Hesychast controversy succeeded to split the Byzantines once again on religious lines, not on the same scale as the Iconoclast controversy of the 8th and 9th centuries, but as the Empire in the 14th century was facing imminent collapse, it was totally superflous and damaging.
Edited by Komnenos - 12-Jul-2006 at 08:19