A kinetic theory of vacuum particle creation under the action of an inertial mechanism is constructed within a nonperturbative dynamical approach. At the semiphenomenological level, the inertial mechanism corresponds to quantum field theory with a time-dependent mass. At the microscopic level, such a dependence may be caused by different reasons: the nonstationary Higgs mechanism, the influence of a mean field or condensate, the presence of the conformal multiplier in the scalar-tensor gravitation theory, etc. In what follows, a kinetic theory in the collisionless approximation is developed for scalar, spinor and massive vector fields in the framework of the oscillator representation, which is an effective tool for transition to the quasiparticle description and for derivation of non-Markovian kinetic equations. Properties of these equations and relevant observables (particle number and energy densities, pressure) are studied. The developed theory is applied here to describe the vacuum matter creation in conformal cosmological models and explain the observed photons number density in the cosmic microwave background radiation. As other example, the self-consistent evolution of scalar fields with nonmonotonic self-interaction potentials (the W potential and Witten-Di Vecchia-Veneziano model) is considered. In particular, conditions for appearance of tachyonic modes and a problem of the relevant definition of a vacuum state are discussed.

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