Related papers: Maximum likelihood estimation for small noise mult…
We study the problem of estimating parameters of the limiting equation of a multiscale diffusion in the case of averaging and homogenization, given data from the corresponding multiscale system. First, we review some recent results that…
In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and…
This paper addresses the problem of estimating the modes of an observed non-stationary mixture signal in the presence of an arbitrary distributed noise. A novel Bayesian model is introduced to estimate the model parameters from the…
Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are…
A continuous-time regression model with a jointly strictly sub-Gaussian random noise is considered in the paper. Upper exponential bounds for probabilities of large deviations of the least squares estimator for the regression parameter are…
Comparison of two univariate distributions based on independent samples from them is a fundamental problem in statistics, with applications in a wide variety of scientific disciplines. In many situations, we might hypothesize that the two…
We consider stochastic non-linear diffusion equations with a highly singular diffusivity term and multiplicative gradient-type noise. We study existence and uniqueness of non-negative variational solutions in terms of stochastic variational…
Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast…
We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin…
We study parameter estimation problem for diagonalizable stochastic partial differential equations driven by a multiplicative fractional noise with any Hurst parameter $H\in(0,1)$. Two classes of estimators are investigated: traditional…
Starting from the simple point process model of 1/f noise we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise in any desirably wide range of frequency. A stochastic differential equation (the general…
We prove the asymptotic normality of the discretized maximum likelihood estimator for the drift parameter in the homogeneous ergodic diffusion model.
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…
We introduce two new particle-based algorithms for learning latent variable models via marginal maximum likelihood estimation, including one which is entirely tuning-free. Our methods are based on the perspective of marginal maximum…
We develop a class of interacting particle systems for implementing a maximum marginal likelihood estimation (MMLE) procedure to estimate the parameters of a latent variable model. We achieve this by formulating a continuous-time…
In this work, we consider the problem of online (real-time, single-shot) estimation of static or slow-varying parameters along quantum trajectories in quantum dynamical systems. Based on the measurement signal of a continuously-monitored…
We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical…
We consider adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones for discretely observed ergodic diffusion processes with observation noise whose variance is constant. The quasi-likelihood functions for the diffusion and…
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
This work is about parameter estimation for a fast-slow stochastic system with non-Gaussian $\alpha$-stable L\'evy noise. When the observations are only available for slow components, a system parameter is estimated and the accuracy for…