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This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…

Methodology · Statistics 2024-01-30 Yuga Iguchi , Alexandros Beskos , Matthew M. Graham

We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with Hurst index 0<H<1/2 and 1/2<H<1. Under some assumptions on the drift coefficient, we…

Statistics Theory · Mathematics 2022-01-04 Shohei Nakajima , Yasutaka Shimizu

Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…

Probability · Mathematics 2019-08-27 Christian Kuehn , Alexandra Neamtu

This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…

Information Theory · Computer Science 2025-06-10 Riccardo Rossetti , Galen Reeves

We consider the numerical approximation of general semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive space-time noise. In contrast to the standard time stepping methods which uses basic increments of…

Numerical Analysis · Mathematics 2010-05-31 Gabriel J. Lord , Antoine Tambue

In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central…

Probability · Mathematics 2024-08-20 Nguyen Tien Dung , Nguyen Thu Hang

In this work we are concerned with the study of the strong order of convergence in the averaging principle for slow-fast systems of stochastic evolution equations in Hilbert spaces with additive noise. In particular the stochastic…

Probability · Mathematics 2023-06-07 Filippo de Feo

This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the…

Numerical Analysis · Mathematics 2020-11-19 Jean Daniel Mukam , Antoine Tambue

The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…

Methodology · Statistics 2018-11-13 Susanne Ditlevsen , Adeline Samson

Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…

Methodology · Statistics 2025-05-20 Qingchuan Sun , Susanne Ditlevsen

This article studies the temporal approximation of hyperbolic semilinear stochastic evolution equations with multiplicative Gaussian noise by Milstein-type schemes. We take the term hyperbolic to mean that the leading operator generates a…

Numerical Analysis · Mathematics 2026-02-03 Felix Kastner , Katharina Klioba

We introduce and test methods for the calibration of the diffusion term in Stochastic Partial Differential Equations (SPDEs) describing fluids. We take two approaches, one uses ideas from the singular value decomposition and the Biot-Savart…

Fluid Dynamics · Physics 2024-05-02 James Woodfield

In this paper we construct a framework for doing statistical inference for discretely observed stochastic differential equations (SDEs) where the driving noise has 'memory'. Classical SDE models for inference assume the driving noise to be…

Methodology · Statistics 2013-07-05 Martin Lysy , Natesh S. Pillai

In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases…

Functional Analysis · Mathematics 2022-05-02 Antonio Agresti , Mark Veraar

Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical…

Numerical Analysis · Mathematics 2023-07-04 Andrea Barth , Andreas Stein

We consider the estimation of a non-linear reaction term in the stochastic heat or more generally in a semi-linear stochastic partial differential equation (SPDE). Consistent inference is achieved by studying a small diffusivity level,…

Statistics Theory · Mathematics 2022-03-22 Sascha Gaudlitz , Markus Reiß

We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…

Numerical Analysis · Mathematics 2018-04-10 Sebastian Krumscheid

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

Computation · Statistics 2012-05-03 Umberto Picchini , Susanne Ditlevsen

In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…

Probability · Mathematics 2016-12-05 Giuseppina Guatteri

We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…

Probability · Mathematics 2015-08-04 David Baños , Paul Krühner