УДК 519.6.57.4 APPROXIMATIVE PROPERTIES OF POLYHARMONIC PROCESSES Polyharmonic approximation for stationary stochastic and harmonized (in Loeve’s sense) processes is consi-dered. <...> The stochastic variant of the Weierstrass theorem is given. <...> Obtained results are compared with the Bohr – Wiener theorem on polyharmonic approximation of almost periodic functions. <...> Some applications to differential equations with constant and periodic parameters are given. <...> Keywords: polyharmonic approximation, stochastic and harmonized processes, theorem Weierstrass, theorem BohrWiener, differential equations. 1. <...> The polyharmonic approximation of harmonized processes Let be the family of random functions second order [1]) such that where function integral . <...> For each , (of - the correlation of the stochastic RSexists and presents certain q. m. continues and q. m. bounded random process (see [1]). <...> A stochastic process there exists is called [1] harmonized if such that . function (1) The set of these processes we denote . <...> Random in (1) is called spectral process (or spectral function) corresponding to given harmonized process . <...> Let us consider process , where , values (frequencies), (2) - determinate - random values of second order. <...> The family of polyharmonic processes we denote . <...> Then for each there exists polyharmonic process (2) such that , , where of process Proof fix , (3) (4) - the correlation of spectral function (1). . <...> In accordance to the definition and certain properties of RS-integral (see [1]) we can conclude that there exist , such that , for all fied, if we put , where , It is clearly that statements (3) and (4) will be satisand . 2. <...> The polyharmonic approximation of stationary stochastic processes A stochastic process wide sense) if depends only on . is called [1] stationary (in , and correlation . <...> The set of these processes we denote . <...> By symbol we shall denote the set of q. m. continues stationary processes. <...> Put tionary if and only if , Proposition 1. <...> Polyharmonic process , Let be the family functions . (2) is sta. such that By let us denote the family of processes with spectral functions Proposition 2 [1]. . 1) Theorem 2. <...> Following statements are equivalent: , 2) for each polyharmonic process Proof implication 1) ond order. <...> If for each (2) with property (3). 2 <...>