相关论文: Variational estimation of the drift for stochastic…

This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic…

Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated…

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 Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes and a priori estimates on the transition…

The Fokker-Planck equations (FPEs) for stochastic systems driven by additive symmetric $\alpha$-stable noises may not adequately describe the time evolution for the probability densities of solution paths in some practical applications,…

We estimate nonparametrically the spatially varying diffusivity of a stochastic heat equation from observations perturbed by additional noise. To that end, we employ a two-step localization procedure, more precisely, we combine local state…

This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…

Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…

Drift is a significant issue that undermines the reliability of gas sensors. This paper introduces a probabilistic model to distinguish between environmental variation and instrumental drift, using low-cost non-dispersive infrared (NDIR)…

The partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. A kernel-type estimators are used for estimation of the quadratic variation of the derivative of the limit of…

Models and methods that are able to accurately and efficiently predict the flows of low-speed rarefied gases are in high demand, due to the increasing ability to manufacture devices at micro and nano scales. One such model and method is a…

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…

Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic…

To characterize the Neumann problem for nonlinear Fokker-Planck equations, we investigate distribution dependent reflecting SDEs (DDRSDEs) in a domain. We first prove the well-posedness and establish functional inequalities for reflecting…

We characterize a stochastic dynamical system with tempered stable noise, by examining its probability density evolution. This probability density function satisfies a nonlocal Fokker-Planck equation. First, we prove a superposition…

We discuss nonparametric estimation of linear multiplier in a trend coefficient in models governed by an $\alpha$-stable small noise.

We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…

We demonstrate that the processes underlying on-line auction price bids and many other longitudinal data can be represented by an empirical first order stochastic ordinary differential equation with time-varying coefficients and a smooth…

Given the importance of continuous-time stochastic volatility models to describe the dynamics of interest rates, we propose a goodness-of-fit test for the parametric form of the drift and diffusion functions, based on a marked empirical…

We survey some of our recent results on existence, uniqueness and regularity of function solutions to parabolic and transport type partial differential equations driven by non-differentiable noises. When applied pathwise to random…