  A general theory of stochastic decision forests reconciling two concepts of
information flow -- decision trees and refined partitions on the one hand,
filtrations from probability theory on the other -- is constructed. The
traditional "nature" agent is replaced with a one-shot lottery draw that
determines a tree of a given decision forest, while each "personal" agent is
equipped with an oracle providing updates on the draw's result and makes
partition refining choices adapted to this information. This theory overcomes
the incapacity of existing approaches to extensive form theory to capture
continuous time stochastic processes like Brownian motion as outcomes of
"nature" decision making in particular. Moreover, a class of stochastic
decision forests based on paths of action indexed by time is constructed,
covering a large fraction of models from the literature and constituting a
first step towards an approximation theory for stochastic differential games in
extensive form.
