We consider the capacity of memoryless finite-state multiple access channel
(FS-MAC) with causal asymmetric noisy state information available at both
transmitters and noisy state information available at the receiver. Single
letter inner and outer bounds are provided for the capacity of such channels
when the state process is independent and identically distributed. The outer
bound is attained by observing that the proposed inner bound is tight for the
sum-rate capacity.

It is known that state-dependent, multi-step Lyapunov bounds lead to greatly
simplified verification theorems for stability, for large classes of Markov
chain models --- This is one component of the ``fluid model'' approach to
stability of stochastic networks. In this paper we extend the general theory to
randomized multi-step Lyapunov theory to obtain criteria for the existence of a
finite steady state, as well as finite moments.