Properties of a Solution of an Inhomogeneous Hyperbolic Equation with Random Right-Hand Side
We consider an inhomogeneous hyperbolic equation with zero initial and boundary conditions and a random centered sample-continuous Gaussian right-hand side. We establish conditions for the existence of a solution of the first boundary-value problem of mathematical physics in the form of a series uniformly convergent in probability in terms of a covariance function. An estimate for the distribution of the supremum of a solution of this problem is obtained.
English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 4, pp 571-582.
Citation Example: Dovhai B. V. Properties of a Solution of an Inhomogeneous Hyperbolic Equation with Random Right-Hand Side // Ukr. Mat. Zh. - 2005. - 57, № 4. - pp. 474–482.