相关论文: Variational estimation of the drift for stochastic…
Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…
This paper introduces a comprehensive extension of the path integral formalism to model stochastic processes with arbitrary multiplicative noise. To do so, It\^o diffusive process is generalized by incorporating a multiplicative noise term…
Unlike many deterministic PDEs, stochastic equations are not amenable to the classical variational theory of Euler-Lagrange. In this paper, we show how self-dual variational calculus leads to solutions of various stochastic partial…
The~numerical solutions to a non-linear Fractional Fokker--Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The~aim is to model anomalous diffusion using an FFP description with fractional velocity…
Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of…
We define power variation estimators for the drift parameter of the stochastic heat equation with the fractional Laplacian and an additive Gaussian noise which is white in time and white or correlated in space. We prove that these…
We derive quantitative estimates for large stochastic systems of interacting particles perturbed by both idiosyncratic and environmental noises, as well as singular kernels. We prove that the (mollified) empirical process converges to the…
In this paper, by establishing the $L^p$-$L^q$ estimate and Sobolev estimates for parabolic partial differential equations with a singular first order term and a Lipschitz first order term, a new Zvonkin-type transformation is given for…
This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
Stochastic volatility modelling of financial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparametric methods for estimation of the…
Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an $\alpha$-stable L\'evy process is still lacking.…
We propose a systematic method to derive the asymptotic behaviour of the persistence distribution, for a large class of stochastic processes described by a general Fokker-Planck equation in one dimension. Theoretical predictions are…
We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed…
The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…
Kernel Estimation is one of the most widely used estimation methods in non-parametric Statistics, having a wide-range of applications, including spot volatility estimation of stochastic processes. The selection of bandwidth and kernel…
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,…
A study of the non-dissipative Brownian motion in vacuum is presented. The noise source associated to the stochastic process assumed in this work is vacuum fluctuations of some quantum field capable of interact with a massive particle. For…