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.

In this paper, we present an application of the stochastic calculusto the problem of modeling electrical networks. The filtering problem have animportant role in the theory of stochastic differential equations(SDEs). In thisarticle, we present an application of the continuous Kalman-Bucy filter for a RLcircuit. The deterministic model of the circuit is replaced by a stochastic model byadding a ...

We introduce the stochastic integration with respect to the infinite-dimensional fractional Brownian motion. Using the techniques of the anticipating stochastic calculus, we derive an Itô formula for Hurst parameter bigger than 1 2 .

An Itô-type formula is given for an asymptotically 4-stable process.

Over the last years, dominating charge carrier transport barrier in silicon heterojunction (SHJ) solar cells could be boiled down to contact of indium–tin oxide (ITO) doped amorphous (a-Si) layer. The formation a parasitic at this junction was hypothesized act as source for deterioration after annealing. However, no experimental proof obtained so far. In contribution, we simultaneously investig...

Based on the concept of sliding mode control, we study the problem of steady state covariance assignment for bilinear stochastic systems. We find that the invariance property of sliding mode control ensures nullity of the matched bilinear term in the system on the sliding mode. By suitably using Ito calculus, the controller u(t) can be designed to force the feedback gain matrix G to achieve the...

Endotracheal tubes (ETTs) constitute a resistive extra load for intubated patients. The ETT pressure drop (DeltaP(ETT)) is usually described by empirical equations that are specific to one ETT only. Our laboratory previously showed that, in adult ETTs, DeltaP(ETT) is given by the Blasius formula (F. Lofaso, B. Louis, L. Brochard, A. Harf, and D. Isabey. Am. Rev. Respir. Dis. 146: 974-979, 1992)...

In this paper, stochastic age-structure population system with jump are studied. It is proved that the semi-implicit Euler approximation solutions converge to the analytic solution for the stochastic age-structured population system with Poisson jump. The analysis use ˆ Ito s ′ formula, Burkholder-DavisGundy's inequality, Gronwall's lemma and some inequalities for our purposes.