This Letter presents a general method for calculation of moments of invariant measure of multidimensional continuous-time dissipative dynamical systems with noise. In particular, moments of the Lorenz model are calculated.PACS 03.40.Gc This Letter addresses the problem of finding the invariant measure (IM) of continuous-time multidimensional dissipative dynamical systems describing hydrodynamical turbulence and some other chaotic phenomena. The dynamical system includes whitenoise terms that correspond to the thermal fluctuations existing in any real fluid; it is shown that without this noise the problem has many solutions and leads to solving a singular system of linear algebraic equations for the moments of the IM. With nonzero noise the system is nonsingular and here it is described how to solve it by a convergent series. The general method is applied to the well-known representative of the dynamical systems describing turbulence, the Lorenz model; this is probably the first time that moments of the Lorenz (or any similar continuous-time multidimensional) system are calculated by a method other than direct numerical integration. Finally, the convergence of the series is discussed.We start with the system of stochastic differential equations dXJdt ~2 Jk X 3 4-r 4-a to accomodate it to the general form (1) dX l /dt=-cr(X l -X 2 )+g l t lf dX 2 /dt--o-X x -X 2 -X x X 3 + g 2 t 2 ,dX 3 /dt = -bX 3 -b(r + a-) + X X X 2 + ftf 3 .From (1) or (6) we can easily obtain a system of linear algebraic equations for the moments (X^1), . . . , (X^N) of the IM (stationary moments). Suppose first that € = 0; hence g^O and the system is deterministic. Since (dX x /dt) = 0, we have from (6) the relation -or (X x ) + a (X 2 ) = 0, and similarly for {dX 2 /dt)~0 and (dX 3 /dt)=0. Also, since (d(X x X 2 )/dt)=0, we have -cr(
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