Investigation of stochastic problems of mathematical physics

The paper is devoted to constructing approximations of the Brownian motion in models leading to stochastic differential equations. For fundamental problems of mathematical physics, namely, for the problem of small vibrations of a string and the problem of heat conduction in a rod, approaches to defining and formalizing random perturbations are shown. For each of these problems, a sequence of random variables is constructed that converges in distribution to the Brownian motion describing random perturbations. The constructed approximations can be used for finding approximate solutions of stochastic problems.