  We leverage commutative hypercomplex analysis to find closed-form solutions
of some systems of stochastic differential equations. Specifically, we obtain
necessary and sufficient conditions under which a system of stochastic
differential equations can be transformed into a scalar one involving processes
valued in a commutative hypercomplex. In the event the targeted scalar
stochastic differential equation is solved by quadratures, we recover the
solution of the original system by projecting the solution of the scalar
stochastic differential equation along the units of the underlying commutative
hypercomplex. The conversion of a system of stochastic differential equations
involving real-valued processes into a scalar one written in terms of
hypercomplex-valued processes is termed hypercomplexification. Both
hypercomplexification and its reverse are mediated by the analyticity of
stochastic differential equations data. They may be iterated in order to
generate higher-dimensional integrable systems of stochastic differential
equations and solve them. We showcase the utility of hypercomplexification by
treating several examples including linear, and linearizable systems of
stochastic differential equations and stochastic Lotka-Volterra systems.
Although we consider only random systems driven by white noises,
hypercomplexification is fundamentally algebraic, and it readily extends to
stochastic systems involving other types of disturbances.
