Spaces of continuous and bounded functions over the field of geometric complex numbers

Following Grossman and Katz (Non-Newtonian Calculus, 1972), we construct the sets and of geometric complex-valued bounded and continuous functions, where A denotes the compact subset of the complex plane a,. We show that the sets and of complex-valued bounded and continuous functions form a vector space with respect to the addition and scalar multiplication in the sense of multiplicative calculus. Finally, we prove that and are complete metric spaces.WOS:0003256373000012-s2.0-8489442673

Approximation of fractional Brownian motion by martingales

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given