相关论文: Stochastic integrals and asymptotic analysis of ca…

We study stochastic perturbations of ODE with stable limit cycles -- referred to as stochastic oscillators -- and investigate the response of the asymptotic (in time) frequency of oscillations to changing noise amplitude. Unlike previous…

We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and non-null cases. The intricate nonlinear interaction of different quantities in SST is…

In this manuscript, we study stochastic comparisons of the second-order statistics from dependent or independent observations with modified proportional hazard rates models. First, we establish the usual stochastic order of the second-order…

The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with emphasis on the analytical formulation of the problem as well as a possible…

Based on the physics of stochastic processes we present a new approach for structural health monitoring. We show that the new method allows for an in-situ analysis of the elastic features of a mechanical structure even for realistic…

This paper presents a central limit theorem for a pre-averaged version of the realized covariance estimator for the quadratic covariation of a discretely observed semimartingale with noise. The semimartingale possibly has jumps, while the…

A class of Fourier based statistics for irregular spaced spatial data is introduced, examples include, the Whittle likelihood, a parametric estimator of the covariance function based on the $L_{2}$-contrast function and a simple…

This paper proposes a methodology to estimate characteristic functions of stochastic differential equations that are defined over polynomials and driven by L\'evy noise. For such systems, the time evolution of the characteristic function is…

Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…

The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…

We study a stochastic Schr{\"o}dinger equation with a quadratic nonlinearity and a space-time fractional perturbation, in space dimension less than 3. When the Hurst index is large enough, we prove local well-posedness of the problem using…

The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…

We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an…

We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at a high temporal frequency, we use limit theorems for multipower variations and…

This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…

Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…

Instrumental variable (IV) methods are widely used to infer treatment effects in the presence of unmeasured confounding. In this paper, we study nonparametric inference with an IV under a separable binary treatment choice model, which…

In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…

We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…

We investigate stochastic Volterra equations and their limiting laws. The stochastic Volterra equations we consider are driven by a Hilbert space valued \Levy noise and integration kernels may have non-linear dependence on the current state…