  In the article random functions in modules over the octonion algebra and
Cayley-Dickson algebras are investigated. For their study transition measures
with values in the octonion algebra and Cayley-Dickson algebras are used.
Stochastic integrals over these algebras are studied. They are applied to
integration of stochastic PDEs. This approach permits subsequently to analyze
and integrate PDEs of orders higher than two of different types including
parabolic, elliptic and hyperbolic.
