Related papers: On a Strictly Decreasing Nonparametric Estimator o…
We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…
Weighted empirical risk minimization is a common approach to prediction under distribution drift. This article studies its out-of-sample prediction error under nonstationarity. We provide a general decomposition of the excess risk into a…
In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…
We study the stochastic diffusive limit of a kinetic radiative transfer equation, which is non-linear, involving a small parameter and perturbed by a smooth random term. Under an appropriate scaling for the small parameter, using a…
We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of…
Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim…
This paper concerns the mathematical analyses of the diffusion model in machine learning. The drift term of the backward sampling process is represented as a conditional expectation involving the data distribution and the forward diffusion.…
We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…
We study the effect of stochastic sampling on the estimation of the drift parameter of continuous time AR(1) process. A natural distribution free moment estimator is considered for the drift based on stochastically observed time points. The…
We introduce verifiable criteria for weak posterior consistency of identifiable Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients in arbitrary dimension.…
We study evolution equations of drift-diffusion type when various parameters are random. Motivated by applications in pedestrian dynamics, we focus on the case when the total mass is, due to boundary or reaction terms, not conserved. After…
We present regularity results for nonlinear drift-diffusion equations of porous medium type (together with their incompressible limit). We relax the assumptions imposed on the drift term with respect to previous results and additionally…
We consider a stochastic differential equation of the form \[dX_t=\theta a(t,X_t)\,dt+\sigma_1(t,X_t)\sigma_2(t,Y_t)\,dW_t\] with multiplicative stochastic volatility, where $Y$ is some adapted stochastic process. We prove…
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…
Estimating function inference is indispensable for many common point process models where the joint intensities are tractable while the likelihood function is not. In this paper we establish asymptotic normality of estimating function…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…
We study the problem of unbiased estimation of expectations with respect to (w.r.t.) $\pi$ a given, general probability measure on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with respect to a standard Gaussian…
Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel,…
This paper studies the limit of a kinetic evolution equation involving a small parameter and driven by a random process which also scales with the small parameter. In order to prove the convergence in distribution to the solution of a…