Regularity of Solutions to Bilinear Stochastic Wave Equations.

The paper is concerned with strong solutions of bilinear stochastic wave equations in [Rscr]d, of which the coefficients contain semimartingale white noises with spatial parameters. For the Cauchy problems, the existence and spatial regularity of solutions in Sobolev spaces are proved under appropriate conditions. The dependence of solution regularity on the smoothness of the random coefficients is ascertained. The proofs are based on stochastic energy inequalities, the semigroup method and certain submartingale inequalities. Regularity results are also obtained for the special case of Wiener semimartingales. [ABSTRACT FROM AUTHOR]