Quenched local central limit theorem for random walks in a time-dependent balanced random environment

We prove a quenched local central limit theorem for continuous-time random walks in ${\mathbb{Z}}^d,d\ge 2$, in a uniformly-elliptic time-dependent balanced random environment which is ergodic under space-time shifts. We also obtain Gaussian upper and lower bounds for quenched and (positive and negative) moment estimates of the transition probabilities and asymptotics of the discrete Green function.