相关论文: Asymptotic Probability Density Function of Nonline…

A Lorentz invariant positive definite expression for photon number density is derived as the absolute square of the invariant scalar product of a polarization sensitive position eigenvector and the photon wave function. It is found that…

In this Letter we analyze the benefit of digital compensation of fiber nonlinearity, where the digital signal processing is divided between the transmitter and receiver. The application of the Gaussian noise model indicates that, where…

Asymptotic equivalence in Le Cam's sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove asymptotic equivalence of such regression…

Stochastic power fluctuation in a fiber optic system due to the interplay among dispersion, nonlinearity and partial coherence of the source is investigated. An analytical expression for the power fluctuation of a signal pulse due to its…

We show that the density of states of random wave equations, normalized by the square of the frequency, has a peak - sometimes narrow and sometimes broad - in the range of wave vectors between the disorder correlation length and the…

The current noise in a multi-probe mesoscopic conductor can have a nonlinear dependence on the strength of driving bias voltage. This paper presents a theoretical formulation for the nonlinear noise spectra. We pay special attention to…

Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties…

Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…

A generic novel model governing optical pulse propagation in a nonlinear dispersive amplifying medium with asymmetric (linear spectral slope) gain is introduced. We examine the properties of asymmetric optical pulses formed in such…

We provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations increasing the multiplicative noise intensity surprisingly…

Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…

Partial wave expansion of the Coulomb-distorted plane wave is determined and studied. Dominant and sub-dominant asymptotic expansion terms are given and leading order three-dimensional asymptotic form is derived. The generalized…

Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with…

To explore resonance phenomena in the nonlinear region, we show by experimental measurements and theoretical analyses that resonance happens in modulation instability (MI) from non-instantaneous nonlinearities in photorefractive crystals.…

Let $\alpha_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the predictive distributions of a sequence $(X_1,X_2,\ldots)$ of $p$-dimensional random vectors. Suppose $$\alpha_n= \mathcal{N} _p (M_n,Q_n)$$ where…

Oscillations and noise are ubiquitous in physical and biological systems. When oscillations arise from a deterministic limit cycle, entrainment and synchronization may be analyzed in terms of the asymptotic phase function. In the presence…

We consider the one-dimensional diffusion of a particle on a semi-infinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker-Planck…

We derive the nonlinear fractional surface wave equation that governs compression waves at an interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective…

There is a well known analogy between the Laughlin trial wave function for the fractional quantum Hall effect, and the Boltzmann factor for the two-dimensional one-component plasma. The latter requires analytic continuation beyond the…

The intensity statistics of signals in the presence of Gaussian noise is obtained by studying the model of a random signal plus a random phasor sum. The additive Gaussian noise is shown to result in a Bessel transform of the probability…