Properties of a Solution of an Inhomogeneous Hyperbolic Equation with Random Right-Hand Side
AbstractWe 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.
How to Cite
DovhaiB. V. “Properties of a Solution of an Inhomogeneous Hyperbolic Equation With Random Right-Hand Side”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, no. 4, Apr. 2005, pp. 474–482, http://umj.imath.kiev.ua/index.php/umj/article/view/3614.