  Many complex systems can be described by population models, in which a pool
of agents interacts and produces complex collective behaviours. We consider the
problem of verifying formal properties of the underlying mathematical
representation of these models, which is a Continuous Time Markov Chain, often
with a huge state space. To circumvent the state space explosion, we rely on
stochastic approximation techniques, which replace the large model by a simpler
one, guaranteed to be probabilistically consistent. We show how to efficiently
and accurately verify properties of random individual agents, specified by
Continuous Stochastic Logic extended with Timed Automata (CSL-TA), and how to
lift these specifications to the collective level, approximating the number of
agents satisfying them using second or higher order stochastic approximation
techniques.
