  We develop a master equation formalism to describe the evolution of the
average density matrix of a closed quantum system driven by a stochastic
Hamiltonian. The average over random processes generally results in decoherence
effects in closed system dynamics, in addition to the usual unitary evolution.
We then show that, for an important class of problems in which the Hamiltonian
is proportional to a Gaussian random process, the 2nd-order master equation
yields exact dynamics. The general formalism is applied to study the examples
of a two-level system, two atoms in a stochastic magnetic field and the heating
of a trapped ion.
