A special stochastic representation of quantum mechanics is proposed. The basis of this representation is the linear combination of soliton solutions to some nonlinear field equations, the particles being identified with the soliton configurations. The wave function of a particle proves to be a vector in the random Hilbert space. The many-particle wave function is constructed via the many-solitons configurations. It is shown that, in the point-like limit when the proper size of the soliton configuration vanishes, the main principles of quantum mechanics are restored. In particular, the expectation values of physical observables are obtained as the Hermitian forms generated by self-conjugated operators and the spin-statistics correspondence stems from the extended character of particles-solitons.

Keywords: stochastic representation, solitons, random Hilbert space

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