Abstract Given a Clifford algebra of arbitrary signature ℓ p,q , p + q = n , multiplicative random walks with dynamic transitions are induced by sequences of random variables taking values in the unit basis vectors and paravectors of the algebra. These walks can be viewed as random walks on “directed hypercubes”. Properties of such multiplicative walks are investigated, and these multiplicative walks are then summed to induce additive walks on the algebra. Properties of both types of walks are considered, and limit theorems are developed.
Advances in Pure and Applied Mathematics – de Gruyter
Published: Mar 1, 2010