The stochastic wave equation driven by fractional Brownian noise and temporally correlated smooth noise

The stochastic wave equation in one spatial dimension driven by a class of fractional noises or, alternately, by a class of smooth noises with arbitrary temporal covariance is studied. In either case, the wave equation is explicitly solved and the upper and lower bounds on both the large and small deviations of several sup norms associated with the solution are given. Finally the energy of a system governed by such an equation is calculated and its expected value is found.