Related papers: A general framework for SPDE-based stationary rand…
The R software package rSPDE contains methods for approximating Gaussian random fields based on fractional-order stochastic partial differential equations (SPDEs). A common example of such fields are Whittle-Mat\'ern fields on bounded…
Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical…
As a concrete setting where stochastic partial differential equations (SPDEs) are able to model real phenomena, we propose a stochastic Meinhardt model for cell repolarisation and study how parameter estimation techniques developed for…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
We introduce computational methods that allow for effective estimation of a flexible, parametric non-stationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field…
Intrinsic Gaussian fields are used in many areas of statistics as models for spatial or spatio-temporal dependence, or as priors for latent variables. However, there are two major gaps in the literature: first, the number and flexibility of…
In this paper, we present a methodology for stability analysis of a general class of systems defined by coupled Partial Differential Equations (PDEs) with spatially dependent coefficients and a general class of boundary conditions. This…
We consider the numerical approximation of Gaussian random fields on closed surfaces defined as the solution to a fractional stochastic partial differential equation (SPDE) with additive white noise. The SPDE involves two parameters…
We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…
Stochastic difference equations and a stochastic partial differential equation (SPDE) are simultaneously derived for the time-dependent neutron angular density in a general three-dimensional medium where the neutron angular density is a…
Obtaining high-resolution maps of precipitation data can provide key insights to stakeholders to assess a sustainable access to water resources at urban scale. Mapping a nonstationary, sparse process such as precipitation at very high…
This paper proposes a methodology to estimate characteristic functions of stochastic differential equations that are defined over polynomials and driven by L\'evy noise. For such systems, the time evolution of the characteristic function is…
We prove a concise and easily verifiable criterion on the existence and global stability of stationary solutions for random dynamical systems (RDSs). As a consequence, we can show that the $\omega$-limit sets of all pullback trajectories of…
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…
In this survey, we provide an in-depth exposition of our recent results on the well-posedness theory for stochastic evolution equations, employing maximal regularity techniques. The core of our approach is an abstract notion of critical…
In this note we provide conditions for local invariance of finite dimensional submanifolds for solutions to stochastic partial differential equations (SPDEs) in the framework of the variational approach. For this purpose, we provide a…
We provide existence and uniqueness of global (and local) mild solutions for a general class of semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures under local Lipschitz and linear…
In this paper we present an $L^p$-theory for the stochastic partial differential equations (SPDEs in abbreciation) driven by L\'e{}vy processes. Existence and uniqueness of solutions in Sobolev spaces are obtained. The coefficients of SPDEs…
The stochastic partial differential equation (SPDE) approach is widely used for modeling large spatial datasets. It is based on representing a Gaussian random field $u$ on $\mathbb{R}^d$ as the solution of an elliptic SPDE $L^\beta u =…
In this paper, we use the variational approach to investigate recurrent properties of solutions for stochastic partial differential equations, which is in contrast to the previous semigroup framework. Consider stochastic differential…