Related papers: Iterated Stochastic Integrals in Infinite Dimensio…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
The solution of a (stochastic) differential equation (SDE) can be locally approximated by a stochastic expansion, a linear combination of iterated integrals. Quantities of interest, like moments, can then be approximated with the expansion.…
The Expectation Maximization (EM) algorithm is of key importance for inference in latent variable models including mixture of regressors and experts, missing observations. This paper introduces a novel EM algorithm, called…
Motivated by applications to multi-antenna wireless networks, we propose a distributed and asynchronous algorithm for stochastic semidefinite programming. This algorithm is a stochastic approximation of a continous- time matrix exponential…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
These notes rigorously construct the stochastic integral of a Hilbert Space valued process driven by a Cylindrical Brownian Motion. We expand upon this stochastic calculus to present an introduction to stochastic differential equations in…
In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…
In this paper, we present a novel local and parallel two-grid finite element scheme for solving the Stokes equations, and rigorously establish its a priori error estimates. The scheme admits simultaneously small scales of subproblems and…
In this article, we extend a Milstein finite difference scheme introduced in [Giles & Reisinger(2011)] for a certain linear stochastic partial differential equation (SPDE), to semi- and fully implicit timestepping as introduced by…
We study parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions with a small dispersion parameter using high frequency data with respect to time and space. We set two…
With a finite amount of measurement data acquired in variational quantum algorithms, the statistical benefits of several optimized numerical estimation schemes, including the scaled parameter-shift (SPS) rule and finite-difference (FD)…
Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…
We consider online statistical inference of constrained stochastic nonlinear optimization problems. We apply the Stochastic Sequential Quadratic Programming (StoSQP) method to solve these problems, which can be regarded as applying…
To obtain strong convergence rates of numerical schemes, an overwhelming majority of existing works impose a global monotonicity condition on coefficients of SDEs. Nevertheless, there are still many SDEs from applications that do not have…
The present paper proposes new fully discrete schemes for long-time approximations of stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients in a bounded domain $D \subset \R^d, d =1,2,3 $. A novel family…
Enforcing exact macroscopic conservation laws, such as mass and energy, in neural partial differential equation (PDE) solvers is computationally challenging in high dimensions. Traditional discrete projections rely on deterministic…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…
Stochastic interpolants offer a robust framework for continuously transforming samples between arbitrary data distributions, holding significant promise for generative modeling. Despite their potential, rigorous finite-time convergence…
We study identification of stochastic Wiener dynamic systems using so-called indirect inference. The main idea is to first fit an auxiliary model to the observed data and then in a second step, often by simulation, fit a more structured…