Related papers: Backward error analysis of stochastic Poisson inte…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
We show that applying any deterministic B-series method of order $p_d$ with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and weak sense with order $\lfloor p_d/2\rfloor$.As an…
We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Statistical solutions have recently been introduced as a an alternative solution framework for hyperbolic systems of conservation laws. In this work we derive a novel a posteriori error estimate in the Wasserstein distance between…
Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient…
We show that, under suitable conditions, finite-dimensional systems describing invariant solutions of partial differential equations (PDEs) inherit local Hamiltonian operators through the mechanism of invariant reduction, which applies…
This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…
We study a family of numerical schemes applied to a class of multiscale systems of stochastic differential equations. When the time scale separation parameter vanishes, a well-known homogenization or Wong--Zakai diffusion approximation…
Phase fitting has been extensively used during the last years to improve the behaviour of numerical integrators on oscillatory problems. In this work, the benefits of the phase fitting technique are embedded in discrete Lagrangian…
For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
In this paper, we propose a new kind of numerical scheme for high-dimensional backward stochastic differential equations based on modified multi-level Picard iteration. The proposed scheme is very similar to the original multi-level Picard…
We develop structure-preserving time integration schemes for Gaussian wave packet dynamics associated with the magnetic Schr\"odinger equation. The variational Dirac--Frenkel formulation yields a finite-dimensional Hamiltonian system for…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
We consider a class of stochastic gradient optimization schemes. Assuming that the objective function is strongly convex, we prove weak error estimates which are uniform in time for the error between the solution of the numerical scheme,…
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…
In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with…
In this paper we propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional $\theta$-scheme, we reduce truncation errors by taking $\theta$ carefully for every subinterval…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…