Some classes of stochastic differential equations for generalized second- order random fields in Banach spaces. (English. Russian original) Zbl 0629.60072

Ponomarenko, A. I.

Theory Probab. Math. Stat. 35, 87-95 (1987); translation from Teor. Veroyatn. Mat. Stat. 35, 78-87 (1986).

The article considers some linear and quasilinear stochastic differential equations of hyperbolic type containing a generalized multiparameter white noise in a Banach space. Existence and uniqueness of solutions is proved using the method of successive approximations. In the linear case, representation of the solution and the first and the second moments are obtained.

Reviewer: K.U.Schaumlöffel

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
60G60	Random fields
35L35	Initial-boundary value problems for higher-order hyperbolic equations
35K60	Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations

Keywords:

stochastic differential equations of hyperbolic type; Existence and uniqueness of solutions