Some linear fractional stochastic equations

Using the multiple stochastic integrals, we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one- and two-parameter cases. When the drift is zero, we show that in the one-parameter case the solution is an exponential—thus positive—function while in the two-parameter setting the solution is negative on a non-negligible set.     

Differentiating σ-fields for Gaussian and shifted Gaussian processes

We study the notions of differentiating and non-differentiating σ-fields in the general framework of (possibly drifted) Gaussian processes and characterize their invariance properties, when changing to an equivalent probability measure. As an application, we investigate the class of stochastic derivatives associated with shifted fractional Brownian motions. We finally establish conditions for the existence of a jointly measurable version of the differentiated process and we outline a general framework for stochastic embedded equations.     

Estimates for the diameter of a martingale

We establish sharp weak type and logarithmic estimates for the diameter of the stopped Brownian motion. Then, using standard embedding theorems, we extend the results to the case of general real-valued continuous-path martingales. The proof rests on finding of the solutions to the corresponding three-dimensional optimal stopping problems.     

On the exponential process associated with a CARMA-type process

We study the correlation decay and the expected maximal increments of the exponential processes determined by continuous-time autoregressive moving average (CARMA)-type processes of order (p, q). We consider two background driving processes, namely fractional Brownian motions and Lévy processes with exponential moments. The results presented in this paper are significant extensions of those very recent works on the Ornstein–Uhlenbeck-type case (p = 1, q = 0), and we develop more refined techniques to meet the general (p, q). In the concluding section, we discuss the perspective role of exponential CARMA-type processes in stochastic modelling of the burst phenomena in telecommunications and the leverage effect in financial econometrics.     

Influence of exchange coupling on current-driven domain wall motion in a nanowire

In this study, the effect of exchange stiffness constant on current-driven domain wall motion in nanowires with in-plane magnetic anisotropy (IMA) and perpendicular magnetic anisotropy (PMA) has been investigated using micromagnetic simulation. The critical current density in a nanowire with IMA decreases as the exchange stiffness constant decreases because the domain wall width at the upper edge of the nanowire narrows according to the decrease of the exchange stiffness constant. On the other hand, the critical current density in a nanowire with PMA slightly decreases contrary to that of IMA although the domain wall width reasonably decreases as the exchange stiffness constant decreases. The slight reduction rate of the critical current density is due to the increase of the effective hard-axis anisotropy of PMA nanowire.     

Time reversal of pseudo-spin 1/2 degrees of freedom

We show that pseudo-spin 1/2 degrees of freedom can be categorized in two types according to their behavior under time reversal. One type exhibits the properties of ordinary spin whose three Cartesian components are all odd under time reversal. For the second type, only one of the components is odd while the other two are even. We discuss several physical examples for this second type of pseudo-spin and highlight observable consequences that can be used to distinguish it from ordinary spin.     

Parameter estimation for chaotic systems with a Drift Particle Swarm Optimization method

Inspired by the motion of electrons in metal conductors in an electric field, we propose a variant of Particle Swarm Optimization (PSO), called Drift Particle Swarm Optimization (DPSO) algorithm, and apply it in estimating the unknown parameters of chaotic dynamic systems. The principle and procedure of DPSO are presented, and the algorithm is used to identify Lorenz system and Chen system. The experiment results show that for the given parameter configurations, DPSO can identify the parameters of the systems accurately and effectively, and it may be a promising tool for chaotic system identification as well as other numerical optimization problems in physics.