  The system of oscillator interacting with vacuum is considered as a problem
of random motion of quantum reactive harmonic oscillator (QRHO). It is
formulated in terms of a wave functional regarded as complex probability
process in the extended space. This wave functional obeys some stochastic
differential equation (SDE). Based on the nonlinear Langevin type SDE of second
order, introduced in the functional space R{W(t)}, the variables in original
equation are separated. The general measure in the space R{W(t)} of the
Fokker-Plank type is obtained and expression for total wave function (wave
mixture) of random QRHO is constructed as functional expansion over the
stochastic basis set. The pertinent transition matrix S_br is constructed. For
Wiener type measure W(t) of functional space the exact representation for
''vacuum-vacuum'' transition probability is obtained. The thermodynamics of
vacuum is described in detail for the asymptotic space R1_as. The exact values
for Energy, shift and expansion of ground state of oscillator and its Entropy
are calculated.
