Related papers: Moderate deviations for recursive stochastic algor…
Sequential analysis encompasses simulation theories and methods where the sample size is determined dynamically based on accumulating data. Since the conceptual inception, numerous sequential stopping rules have been introduced, and many…
This paper investigates a class of slow--fast systems of rough partial differential equations defined over a monotone family of interpolation Hilbert spaces. By employing the controlled rough path framework tailored to a monotone family of…
This article derives lower bounds on the convergence rate of continuous-time gradient-based optimization algorithms. The algorithms are subjected to a time-normalization constraint that avoids a reparametrization of time in order to make…
We apply duality theory to discretized convex minimization problems to obtain computable guaranteed upper bounds for the distance of given discrete functions and the exact discrete minimizer. Furthermore, we show that the discrete duality…
In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
In this paper, we study small noise asymptotics of Markov-modulated diffusion processes in the regime that the modulating Markov chain is rapidly switching. We prove the joint sample-path large deviations principle for the Markov-modulated…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
The time discretization of stochastic spectral fractional wave equation is studied by using the difference methods. Firstly, we exploit rectangle formula to get a low order time discretization, whose the strong convergence order is smaller…
Time delay estimation has long been an active area of research. In this work, we show that compressive sensing with interpolation may be used to achieve good estimation precision while lowering the sampling frequency. We propose an…
Time delay estimation plays a critical role in control, stabilization and state estimation of many practical system with time delay. In this paper, we propose a method to estimate delay for discrete time linear multiple-input…
This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential…
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the…
Two fast L1 time-stepping methods, including the backward Euler and stabilized semi-implicit schemes, are suggested for the time-fractional Allen-Cahn equation with Caputo's derivative. The time mesh is refined near the initial time to…
Richardson extrapolation is applied to a simple first-order upwind difference scheme for the approximation of solutions of singularly perturbed convection-diffusion problems in one dimension. Robust a posteriori error bounds are derived for…
We establish Cram\'er-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are…
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…
In this paper, we establish the large deviation principle for 3D stochastic primitive equations with small perturbation multiplicative noise. The proof is mainly based on the weak convergence approach.
Probabilistic programs with mixed support (both continuous and discrete latent random variables) commonly appear in many probabilistic programming systems (PPSs). However, the existence of the discrete random variables prohibits many basic…
We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…