Octonion random functions and integration of stochastic PDEs

Abstract

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.