Related papers: Statistical inference for discretely sampled stoch…
This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and…
We will consider the following stochastic differential equation (SDE): \begin{equation} X_t=X_0+\int_0^tb(X_s,\theta_0)ds+\sigma B_t,~~~t\in(0,T], \end{equation} where $\{B_t\}_{t\ge 0}$ is a fractional Brownian motion with Hurst index…
We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required…
This paper deals with the consistency and a rate of convergence for a Nadaraya-Watson estimator of the drift function of a stochastic differential equation driven by an additive fractional noise. The results of this paper are obtained via…
We consider a general multidimensional stochastic differential delay equation (SDDE) with state-dependent colored noises. We approximate it by a stochastic differential equation (SDE) system and calculate its limit as the time delays and…
We consider a problem of statistical estimation of an unknown drift parameter for a stochastic differential equation driven by fractional Brownian motion. Two estimators based on discrete observations of solution to the stochastic…
Diffusion models, typically formulated as discretizations of stochastic differential equations (SDEs), have achieved state-of-the-art performance in generative tasks. However, their theoretical analysis often involves complex proofs. In…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
We consider statistical inference for a class of dynamic mixed-effect models described by stochastic differential equations whose drift and diffusion coefficients simultaneously depend on fixed- and random-effect parameters. Assuming that…
We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with respect to a known equilibrium density. In Tupper and Yang…
The aim of this paper is to develop tractable large deviation approximations for the empirical measure of a small noise diffusion. The starting point is the Freidlin-Wentzell theory, which shows how to approximate via a large deviation…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a…
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…
We consider delay differential equations (DDE) that are on the verge of an instability, i.e. the characteristic equation for the linearized equation has one root as zero and all other roots have negative real parts. In presence of small…
In this paper, we consider parameter estimation for stochastic differential equations driven by Wiener processes and compound Poisson processes. We assume unknown parameters corresponding to coefficients of the drift term, diffusion term,…
The article introduces spatial long-range dependent models based on the fractional difference operators associated with the Gegenbauer polynomials. The results on consistency and asymptotic normality of a class of minimum contrast…
A fully discrete finite difference scheme for stochastic reaction-diffusion equations driven by a $1+1$-dimensional white noise is studied. The optimal strong rate of convergence is proved without posing any regularity assumption on the…
We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the…