In this paper, we start the study of stochastic processes over the skew field of quaternions. We discuss the relation between positive definite functions and the covariance of centered Gaussian processes and the construction of stochastic processes and their derivatives. The use of perfect spaces and strong algebras and the notion of Fock space are crucial in this framework.
D. Alpay, F. Colombo, and I. Sabadini. On a class of quaternionic positive definite functions and their derivatives. Journal of Mathematical Physics, vol. 58 (2017), no. 3, 033501, 15 pp.