Stochastic perturbation of wave equations
Maged Elshamy · Stochastic Analysis and Applications · 1994
We consider a wave equation with non-linear random forcing of the form .If the initial conditions are of sufficient regularity the solution uεis shown to be Hölder continuous of exponent. kfor some 0<k< 1/2.The small stochastic perturbation relates to random effects which are often ignored. As the intensity of the stochastic perturbation tends to zero the distribution of uε decays exponentially outside of any neighborhood of the solution of the unperturbed equation Large deviations principle for εin terms of Freidlin-Wentzel estimates is obtained in the Hölder's norm of exponent κ, for some k∊[0,1/2)