INCREMENTS AND DIFFERENTIALS IN THE STOCHASTIC ANALYSIS OF FRACTIONAL DIFFERENTIAL EQUATIONS

摘要

A clear definition of increments and differentials in the case of fractional differential equations enforced by white noise processes is of fundamental importance for the probabilistic characterization of the response process. In this paper it is shown that the incrementsfor equations of the kind (D~α X)(t) = W(t) where α is the order of fractional derivative and W(t) is a white noise process, strictly depend on the order of the fractional derivative at hand. It is shown that increments may be of order dt and thus range from ∞ up to dt~(1.5) as a = 2 and so on.