Particle production in cosmology and imaginary time method

After brief personal recollections of the author's long-time friendship with Misha Marinov the problem of particle production by classical time- varying scalar field is discussed. In the quasiclassical limit the calculations are done by imaginary time method developed, in particular, in Marinov's works. The method permits to obtain simple analytical expressions which well agree with the later found numerical solutions. The results are compared with perturbative calculations and it is argued that perturbation theory gives an upper limit for the rate of production.