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.
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].