ABSTRACT
Partial differential equations of the first order involving one single unknown function are regarded as the simplest ones to study. As is well known, in the deterministic case, integration of such an equation can be reduced to solving a family of ordinary differential equations. This chapter deals with linear and quasilinear first-order equations with coefficients being finite-dimensional, spatially dependent white noises. In the deterministic case the method of characteristics is commonly applied to the first-order hyperbolic systems. The generalization of the scalar equation to a stochastic hyperbolic system has not been done. In particular it is of interest to determine what type of random coefficients is admitted so that the Cauchy problems of a stochastic hyperbolic system are well posed. By confining to finite-dimensional white-noises, the chapter shows that some first-order stochastic partial differential equations can be solved by the method of ordinary Ito equations.
