On Stochastic Variation in Discrete Time Systems

摘要

This paper concerns with the variation in discrete time systems driven by a random walk, in contrast with the ordinary Malliavin calculus based on a Brownian motion. A derivative of random functionals with respect to a random walk is introduced and some its fundamental properties are shown. Theories parallel to Malliavin calculus are also discussed in view of applications for discrete time phenomena in signal processing, mathematical finance, and systems science and engineering.