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.