What is the connection between Random Forest and stochastic process theory?

Random Forest can be modeled as an expectation over a stochastic tree-generating process.

Each tree is a realization of a stochastic process driven by bootstrapped data and random feature selection. The RF predictor is an empirical expectation over this process. This connects RF to Monte Carlo methods and stochastic approximation theory, where convergence depends on independence and identical distribution of tree-generating randomness.