  The simulation of chemical kinetics involving multiple scales constitutes a
modeling challenge (from ordinary differential equations to Markov chain) and a
computational challenge (multiple scales, large dynamical systems, time step
restrictions). In this paper we propose a new discrete stochastic simulation
algorithm: the postprocessed second kind stabilized orthogonal $\tau$-leap
Runge-Kutta method (PSK-$\tau$-ROCK). In the context of chemical kinetics this
method can be seen as a stabilization of Gillespie's explicit $\tau$-leap
combined with a postprocessor. The stabilized procedure allows to simulate
problems with multiple scales (stiff), while the postprocessing procedure
allows to approximate the invariant measure (e.g. mean and variance) of ergodic
stochastic dynamical systems. We prove stability and accuracy of the
PSK-$\tau$-ROCK. Numerical experiments illustrate the high reliability and
efficiency of the scheme when compared to other $\tau$-leap methods.
