  We discuss particle production associated with vacuum decay, which changes
the mass of a scalar field coupled to a background field which induces the
decay. By utilizing the Stokes phenomenon, we can optimally track the
time-evolution of mode function and hence calculate particle production
properly. In particular, we use real time formalisms for vacuum decay in
Minkowski and de Sitter spacetime together with the Stokes phenomenon method.
For each case, we consider the flyover vacuum decay model and stochastic
inflation, respectively. Within the real time formalism, the particle
production can be viewed as that caused by nontrivial external fields. This
gives us a novel perspective of the real time formalism of vacuum decay.
