We analyze Jackiw-Teitelboim gravity as a stochastic process, with a random variable that takes values in AdS_2 viewed as a measure space. We formulate a conjecture in which the variational problem solved by Einstein's equations is identified with a stationarity condition for classical probability distributions induced by the quantum dynamics of the boundary. The dilaton solution, or area of compactified space, is identified with a stationary probability distribution from the perspective of the boundary system. We describe calculations in progress to verify the conjecture.