We develop a stochastic calculus that makes it easy to capture variety of predictable transformations semimartingales such as changes variables, integrals, and their compositions. The framework offers unified treatment real-valued complex-valued semimartingales. proposed is blueprint for the derivation new relationships among processes with specific examples provided below.

A stochastic calculus is given for processes described by integrals with respect to fractional Brownian motions and Rosenblatt somewhat analogous the Itô processes. These this arise naturally from a chain rule functionals of processes; some Itô-type expressions are here. Furthermore, there analysis these results their applications problems using noise.

Since the fractional Brownian motion is not a semi–martingale, the usual Ito calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the Itô–Clark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.

Since the fractional Brownian motion is not a semiimartingale, the usual Ito calculus cannot be used to deene a full stochastic calculus. However, in this work, we obtain the Itt formula, the ItttClark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.

A basic calculus is presented for stochastic service guarantee analysis in communication networks. Central to the calculus are two definitions, maximum-(virtual)-backlog-centric (m.b.c) stochastic arrival curve and stochastic service curve, which respectively generalize arrival curve and service curve in the deterministic network calculus framework. With m.b.c stochastic arrival curve and stoch...