  Causal ordering of key events in the cell cycle is essential for proper
functioning of an organism. Yet, it remains a mystery how a specific temporal
program of events is maintained despite ineluctable stochasticity in the
biochemical dynamics which dictate timing of cellular events. We propose that
if a change of cell fate is triggered by the {\em time-integral} of the
underlying stochastic biochemical signal, rather than the original signal, then
a dramatic improvement in temporal specificity results. Exact analytical
results for stochastic models of hourglass-timers and pendulum-clocks, two
important paradigms for biological timekeeping, elucidate how temporal
specificity is achieved through time-integration. En route, we introduce a
natural representation for time-integrals of stochastic processes, provide an
analytical prescription for evaluating corresponding first-passage-time
distributions, and uncover a mechanism by which a population of identical cells
can spontaneously bifurcate into subpopulations of early and late responders,
depending on hierarchy of timescales in the dynamics. Moreover, our approach
reveals how time-integration of stochastic signals may be realized
biochemically, through a simple chemical reaction scheme.
