On the method of moment functions in the stochastic Helmholtz problem (Q2719395)

The paper addresses systems of linear (with respect to drift) stochastic second-order Ito equations NEWLINE\[NEWLINE\ddot x_i = a_{ik}(t)\dot x_k + b_{ik}(t)x_k + \sigma_{ij}(t,x,\dot x)\dot\xi^j, \qquad i= 1,\dots, n,\quad j= 1, \dots, m, \tag{1} NEWLINE\]NEWLINE where \(\xi^1(t),\xi^2(t),\dots,\xi^m(t)\) is the system of Wiener processes with an identity matrix of local dispersions. The author proposes a method of constructing the equations of the Lagrange structure for system (1) in the spaces of moment functions of first (second) order. Examples of the general technique application are presented.