Let the Ornstein–Uhlenbeck process $$(X_t)_{t\ge 0}$$ driven by a fractional Brownian motion $$B^{H }$$ described $$dX_t = -\theta X_t dt + \sigma dB_t^{H be observed at discrete time instants $$t_k=kh$$ , $$k=0, 1, 2, \ldots 2n+2 $$ . We propose an ergodic type statistical estimator $${\hat{\theta }}_n $${\hat{H}}_n and $${\hat{\sigma to estimate all parameters $$\theta H $$\sigma in above mod...

The widely used split-step Fourier method has difficulties when solving partial differential equations with saturable gain. Here, we describe a modified split-step Fourier method, and we compare it to several different algorithms for solving the Haus mode-locking equation and related equations that are used to model mode-locked lasers and other optical oscillators and amplifiers with saturable ...

This paper solves the Non Linear Schrodinger Equation using the Split Step Fourier method for modeling an optical fiber. The model generates a complex wave of optical pulses and using the results obtained two graphs namely Loss versus Wavelength and Dispersion versus Wavelength are generated. Taking Chromatic Dispersion and Polarization Mode Dispersion losses into account, the graphs generated ...

The phase-screen and the split-step Fourier methods, which allow modeling and migration in laterally heterogeneous media, are generalized here so as to increase their accuracies for media with large and rapid lateral variations. The medium is defined in terms of a background medium and a perturbation. Such a contrast formulation induces a series expansion of the vertical slowness in which we re...

30 Children show precocious ability in the learning of languages; is this the case with motor 31 learning? We used split-belt walking to probe motor adaptation (a form of motor 32 learning) in children. Data from 27 children (aged 8-36 months) were compared with 33 that from 10 adults. Children walked with the treadmill belts at the same speed (tied34 belt), followed by walking with the belts m...

Typical information processing is thought to depend on the integrity of neurobiological oscillations that may underlie coordination and timing of cells and assemblies within and between structures. The 3-7 Hz bandwidth of hippocampal theta rhythm is associated with cognitive processes essential to learning and depends on the integrity of cholinergic, GABAergic, and glutamatergic forebrain syste...