相关论文: Statistical properties of a filtered Poisson proce…

Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…

In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…

We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target…

When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…

We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in stochastic processes using lower dimensional projections. Our model combines the techniques…

This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…

The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here…

We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally…

Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…

Existing algorithms for fitting the parameters of a sinusoid to noisy discrete time observations are not always successful due to initial value sensitivity and other issues. This paper demonstrates the techniques of FIR filtering, Fast…

Shot-noise and fractional Poisson processes are instances of filtered Poisson processes. We here prove Girsanov theorem for this kind of processes and give an application to an estimate problem.

We study the estimation of moments and joint moments of microstructure noise. Estimators of arbitrary order of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In particular, we provide…

Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. Practical observations, however, often contain compositional noise, i.e. a nonlinear shift along the time axis,…

We consider the problem of estimating unknown parameters in stochastic differential equations driven by colored noise, which we model as a sequence of Gaussian stationary processes with decreasing correlation time. We aim to infer…

In this paper, we study a simple correlation-based strategy for estimating the unknown delay and amplitude of a signal based on a small number of noisy, randomly chosen frequency-domain samples. We model the output of this "compressive…

The matched filter (MF) is widely used to detect signals hidden within the noise. If the noise is Gaussian, its performances are well-known and describable in an elegant analytical form. The treatment of non-Gaussian noises is often…

The statistical properties of nonlinear phase noise, often called the Gordon-Mollenauer effect, is studied analytically when the number of fiber spans is very large. The joint characteristic functions of the nonlinear phase noise with…

We consider the origin of noise and distortions in power spectral estimates of randomly sampled data, specifically velocity data measured with a burst-mode laser Doppler anemometer. The analysis guides us to new ways of reducing noise and…

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…

In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…