Has the same relation to DSPACE(f(n)) as PP does to P. The Turing machine has to halt with probability 1 on every input.
Contained in DSPACE(f(n)2) [BCP83].
Equals PrHSPACE(f(n)) [Jun85].
Has the same relation to DSPACE(f(n)) as PP does to P. The Turing machine has to halt on every input and every setting of the random tape.