Related papers: Parametric estimation for linear parabolic SPDEs i…
The strong numerical approximation of semilinear stochastic partial differential equations (SPDEs) driven by infinite dimensional Wiener processes is investigated. There are a number of results in the literature that show that Euler-type…
Second-order variational type equations for spatial point processes are established. In case of log linear parametric models for pair correlation functions, it is demonstrated that the variational equations can be applied to construct…
We establish the unique solvability of solutions in Sobolev spaces to linear parabolic equations in a more general form than those in the literature. A distinguishing feature of our equations is the inclusion of a half-order time derivative…
We present a hybrid quantum-classical framework for solving general time-dependent parabolic partial differential equations (PDEs) using quantum variational circuits. Building on the QPINN approach, this method applies broadly to parabolic…
We discuss the problem of parameter estimation in nonlinear stochastic differential equations based on sampled time series. A central message from the theory of integrating stochastic differential equations is that there exists in general…
Parareal is a well-studied algorithm for numerically integrating systems of time-dependent differential equations by parallelising the temporal domain. Given approximate initial values at each temporal sub-interval, the algorithm locates a…
A partially linear probit model for spatially dependent data is considered. A triangular array setting is used to cover various patterns of spatial data. Conditional spatial heteroscedasticity and non-identically distributed observations…
A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in…
We consider a class of parabolic semi-linear stochastic partial differential equations driven by space-time white noise on a compact space interval. Our aim is to obtain precise asymptotics of the transition times between metastable states.…
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…
Image based diagnostics are interpreted in the context of spatial resolution. The same is true for tomographic image reconstruction. Current empirically driven approaches to quantify spatial resolution rely on a deterministic formulation…
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…
We propose a bivariate quantile regression method for the bivariate varying coefficient model through a directional approach. The varying coefficients are approximated by the B-spline basis and an $L_{2}$ type penalty is imposed to achieve…
We investigate pointwise estimation of the function-valued velocity field of a second-order linear SPDE. Based on multiple spatially localised measurements, we construct a weighted augmented MLE and study its convergence properties as the…
Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…
The problem of estimating the parameters of a linear regression model $Z(s,t)=m_1g_1(s,t)+ \cdots + m_pg_p(s,t)+U(s,t)$ based on observations of $Z$ on a spatial domain $G$ of special shape is considered, where the driving process $U$ is a…
This article is devoted to the analysis of semilinear, parabolic, Stochastic Partial Differential Equations, with slow and fast time scales. Asymptotically, an averaging principle holds: the slow component converges to the solution of…
In this study, we investigate estimation and inference on a low-dimensional causal parameter in the presence of high-dimensional controls in an instrumental variable quantile regression. Our proposed econometric procedure builds on the…
This paper introduces SPDE bridges with observation noise and contains an analysis of their spatially semidiscrete approximations. The SPDEs are considered in the form of mild solutions in an abstract Hilbert space framework suitable for…