Related papers: Averaging for stochastic perturbations of integrab…
Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of…
We establish a general framework to study the rate of convergence of a Euler type approximation scheme with decreasing time steps to the invariant measure, for a general class of stochastic systems. The error is measured in general…
A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scientific background this was motivated by applications and…
We study the long-term average evolution of the random ensemble along integrable Hamiltonian systems with time $T$-periodic transitions. More precisely, for any observable $G$, it is demonstrated that the ensemble under $G$ in long time…
We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in $L^1$ and $L^\infty$ norms depending on the…
Our work is part of the close link between continuous-time dissipative dynamical systems and optimization algorithms, and more precisely here, in the stochastic setting. We aim to study stochastic convex minimization problems through the…
Equation with the symmetric integral with respect to stochastic measure is considered. For the integrator, we assume only $\sigma$-additivity in probability and continuity of the paths. It is proved that the averaging principle holds for…
We examine the convergence in the Krylov--Bogolyubov averaging for nonlinear stochastic perturbations of linear PDEs with pure imaginary spectrum and show that if the involved effective equation is mixing, then the convergence is uniform in…
We analyze nonequilibrium fluctuations of the averaging process on $\mathbb T_\varepsilon^d$, a continuous degenerate Gibbs sampler running over the edges of the discrete $d$-dimensional torus. We show that, if we start from a smooth…
In a separable Hilbert space, we study the minimization problem of a convex smooth function with Lipschitz continuous gradient whose evaluations are corrupted by random noise. To this end, we associate a stochastic inertial system that…
The Einstein vacuum equations on an (n+1)-dimensional toroidal manifold $\mathbb{M}^{n+1}=\mathbb{T}^{n}\times\mathbb{R}^{+}$ reduce to a system of n-dimensional nonlinear ODEs in terms of the set of toroidal radii $(a_{i})_{i=1}^{n}$ or…
We compare the rate of convergence to the time average of a function over an integrable Hamiltonian flow with the one obtained by a stochastic perturbation of the same flow. Precisely, we provide detailed estimates in different Fourier…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…
Stochastic non-smooth convex optimization constitutes a class of problems in machine learning and operations research. This paper considers minimization of a non-smooth function based on stochastic subgradients. When the function has a…
Consider an SDE on a foliated manifold whose trajectories lay on compact leaves. We investigate the effective behavior of a small transversal perturbation of order $\varepsilon$. An average principle is shown to hold such that the component…
We consider the problem of closeness of solutions of an exact and an averaged difference equations on an infinite interval. Appropriate assertions are derived from one special theorem on the stability under constantly acting perturbations.
We consider stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme…
This paper investigates the asymptotic behavior of stochastic recursive inclusions in the presence of non-zero, non-diminishing bias, a setting that frequently arises in zeroth-order optimization, stochastic approximation with…