### A Stability Property of Stochastic Vibration

M. Elshamy
2007 Journal of Applied Probability
Let u(t,x) be the displacement at time t of a point x on a string; the time variable t varies in the interval I≔[0,T] and the space variable x varies in the interval J≔[0,L], where T and L are fixed positive constants. The displacement u(t,x) is the solution to a stochastic wave equation. Two forms of random excitations are considered, a white noise in the initial condition and a nonlinear random forcing which involves the formal derivative of a Brownian sheet. In this article, we consider the
more » ... ontinuity properties of solutions to this equation. Smoothness characteristics of these random fields, in terms of Hölder continuity, are also investigated.
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