Related papers: Discretization Error of Stochastic Iterated Integr…
This work is devoted to convergence analysis of an exponential integrator scheme for semi-discretization in time of nonlinear stochastic wave equation. A unified framework is first set forth, which covers important cases of additive and…
In this paper we lay the foundation for a numerical algorithm to simulate high-dimensional coupled FBSDEs under weak coupling or monotonicity conditions. In particular, we prove convergence of a time discretization and a Markovian…
We consider a sequence $X^n=(X^n_t)_{t\ge 0},n\ge 1$ of semimartingales. Each $X^n$ is a weak solution to an It\^o equation with respect to a Wiener process and a Poissonian martingale measure and is in general non-Markovian process. For…
We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence,…
We study pathwise approximation of scalar stochastic differential equations at a single point. We provide the exact rate of convergence of the minimal errors that can be achieved by arbitrary numerical methods that are based (in a…
We consider stochastic optimization problems where the objective depends on some parameter, as commonly found in hyperparameter optimization for instance. We investigate the behavior of the derivatives of the iterates of Stochastic Gradient…
A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be…
We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…
The optimal rate of convergence of estimators of the integrated volatility, for a discontinuous It\^{o} semimartingale sampled at regularly spaced times and over a fixed time interval, has been a long-standing problem, at least when the…
We propose a novel discrete Poisson equation approach to estimate the statistical error of a broad class of numerical integrators for the underdamped Langevin dynamics. The statistical error refers to the mean square error of the estimator…
In this work we establish weak convergence rates for temporal discretisations of stochastic wave equations with multiplicative noise, in particular, for the hyperbolic Anderson model. For this class of stochastic partial differential…
In this paper we construct a framework for doing statistical inference for discretely observed stochastic differential equations (SDEs) where the driving noise has 'memory'. Classical SDE models for inference assume the driving noise to be…
We study integrodifferential operators and regularity estimates for solutions to integrodifferential equations. Our emphasis is on kernels with a critically low singularity which does not allow for standard scaling. For example, we treat…
This paper considers a stochastic approximation algorithm, with decreasing step size and martingale difference noise. Under very mild assumptions, we prove the non convergence of this process toward a certain class of repulsive sets for the…
We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\^o calculus, such…
We establish the rate of convergence in the $L^1$-norm for equidistant approximations of stochastic integrals with discontinuous integrands driven by multifractional Brownian motion. Our findings extend the known results for the case when…
We consider the goal-oriented error estimates for a linearized iterative solver for nonlinear partial differential equations. For the adjoint problem and iterative solver we consider, instead of the differentiation of the primal problem, a…
Stochastic gradient descent (SGD) is widely believed to perform implicit regularization when used to train deep neural networks, but the precise manner in which this occurs has thus far been elusive. We prove that SGD minimizes an average…
Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel,…
We address our attention to the numerical time discretization of stochastic Poisson systems via Poisson integrators. The aim of the investigation regards the backward error analysis of such integrators to reveal their ability of being…