Related papers: A tamed-adaptive Milstein scheme for stochastic di…

We study the convergence of a generic tamed Euler-Maruyama (EM) scheme for the kinetic type stochastic differential equations (SDEs) (also known as second order SDEs) with singular coefficients in both weak and strong probabilistic senses.…

In this paper, we introduce adaptive Euler-Maruyama schemes for McKean-Vlasov stochastic differential equations (SDEs) assuming only a standard monotonicity condition on the drift and diffusion coefficients but no global Lipschitz…

For the Euler scheme of the stochastic linear evolution equations, discrete stochastic maximal $ L^p $-regularity estimate is established, and a sharp error estimate in the norm $ \|\cdot\|_{L^p((0,T)\times\Omega;L^q(\mathcal O))} $, $ p,q…

We propose a new adaptive algorithm for the approximation of the Landau-Lifshitz-Gilbert equation via a higher-order tangent plane scheme. We show that the adaptive approximation satisfies an energy inequality and demonstrate numerically,…

We prove stability and convergence of a full discretization for a class of stochastic evolution equations with super-linearly growing operators appearing in the drift term. This is done using the recently developed tamed Euler method, which…

We establish an optimal strong convergence rate of a fully discrete numerical scheme for second order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen-Cahn equation, driven by an…

In this article we show that for SDEs with a drift coefficient that is non-locally integrable, one may define a tamed Euler scheme that converges in $L^p$ at rate $1/2$ to the true solution. The taming is required in this case since one…

The author presented a stochastic and variational approach to the Lax-Friedrichs finite difference scheme applied to hyperbolic scalar conservation laws and the corresponding Hamilton-Jacobi equations with convex and superlinear…

We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…

One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…

We consider the problem of training a deep neural network with nonsmooth regularization to retrieve a sparse and efficient sub-structure. Our regularizer is only assumed to be lower semi-continuous and prox-bounded. We combine an adaptive…

This paper is devoted to the convergence analysis of stochastic approximation algorithms of the form $\theta\_{n+1} = \theta\_n + \gamma\_{n+1} H\_{\theta\_n}(X\_{n+1})$ where $\{\theta\_nn, n \geq 0\}$ is a $R^d$-valued sequence,…

Recently there has been renewed interests in derivative free approaches to stochastic optimization. In this paper, we examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various…

We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive grid-based stochastic approximation strategy which…

In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…

In this contribution, we provide convergence rates for a finite volume scheme of a stochastic non-linear parabolic equation with multiplicative Lipschitz noise and homogeneous Neumann boundary conditions. More precisely, we give an error…

We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a…

We investigate the error of the randomized Milstein algorithm for solving scalar jump-diffusion stochastic differential equations. We provide a complete error analysis under substantially weaker assumptions than known in the literature. In…

We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result…

While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…