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In recent years, many design automation methods have been developed to routinely create approximate implementations of circuits and programs that show excellent trade-offs between the quality of output and required resources. This paper…

Neural and Evolutionary Computing · Computer Science 2021-08-17 Lukas Sekanina

We propose a straightforward and effective method for discretizing multi-dimensional diffusion processes as an extension of Milstein scheme. The new scheme is explicitly given and can be simulated using Gaussian variates, requiring the same…

Numerical Analysis · Mathematics 2024-09-04 Yuga Iguchi , Toshihiro Yamada

We consider the energy saving approximation of a Wiener process under unilateral constraints. We show that, almost surely, on large time intervals the minimal energy necessary for the approximation logarithmically depends on the interval's…

Probability · Mathematics 2023-06-26 M. A. Lifshits , S. E. Nikitin

We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…

Probability · Mathematics 2018-02-20 Vincent Lemaire

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian…

Optimization and Control · Mathematics 2016-02-23 Jesper Karlsson , Stig Larsson , Mattias Sandberg , Anders Szepessy , Raùl Tempone

In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is a unnormalized probability density function of the filter…

Numerical Analysis · Mathematics 2022-11-29 Fengshan Zhang , Yongkui Zou , Shimin Chai , Yanzhao Cao

We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…

Probability · Mathematics 2013-02-01 Max Fathi , Noufel Frikha

Modeling real processes often results in several suitable models. In order to be able to distinguish, or discriminate, which model best represents a phenomenon, one is interested, e.g., in so-called T-optimal designs. These consist of the…

Optimization and Control · Mathematics 2022-08-30 David Mogalle , Philipp Seufert , Jan Schwientek , Michael Bortz , Karl-Heinz Küfer

We consider the closely related problems of sampling from a distribution known up to a normalizing constant, and estimating said normalizing constant. We show how variational autoencoders (VAEs) can be applied to this task. In their…

Machine Learning · Computer Science 2022-09-22 George T. Cantwell

We consider a one-dimensional stochastic differential equation driven by a Wiener process, where the diffusion coefficient depends on an ergodic fast process. The averaging principle is satisfied: it is well-known that the slow component…

Probability · Mathematics 2021-04-30 Charles-Edouard Bréhier

In this paper we derive weak limits for the discretization errors of sampling barrier-hitting and extreme events of Brownian motion by using the Euler discretization simulation method. Specifically, we consider the Euler discretization…

Probability · Mathematics 2017-08-16 A. B. Dieker , Guido Lagos

We treat the change point problem in ergodic diffusion processes from discrete observations. Tonaki et al. (2020) proposed adaptive tests for detecting changes in the diffusion and drift parameters in ergodic diffusion models. When any…

Statistics Theory · Mathematics 2021-02-16 Yozo Tonaki , Yusuke Kaino , Masayuki Uchida

In this paper we show that the rate of convergence of Wong-Zakai approximations for stochastic partial differential equations driven by Wiener processes is essentially the same as the rate of convergence of the driving processes W_n…

Probability · Mathematics 2012-09-14 I. Gyöngy , P. R. Stinga

The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…

Probability · Mathematics 2026-04-14 Benjamin Seeger

In this paper we deal with pointwise approximation of solutions of stochastic differential equations (SDEs) driven by infinite dimensional Wiener process with additional jumps generated by Poisson random measure. The further investigations…

Probability · Mathematics 2022-05-04 Paweł Przybyłowicz , Michał Sobieraj , Łukasz Stȩpień

We study the approximation of $\mathbb{E}f(X_T)$ by a Monte Carlo algorithm, where $X$ is the solution of a stochastic differential equation and $f$ is a given function. We introduce a new variance reduction method, which can be viewed as a…

Probability · Mathematics 2007-05-23 Ahmed Kebaier

In this paper, we study a method to sample from a target distribution $\pi$ over $\mathbb{R}^d$ having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler…

Statistics Theory · Mathematics 2016-12-20 Alain Durmus , Eric Moulines

We consider a decision maker who must choose an action in order to maximize a reward function that depends also on an unknown parameter {\Theta}. The decision maker can delay taking the action in order to experiment and gather additional…

Machine Learning · Statistics 2021-06-22 Victor F. Araman , Rene Caldentey

This paper considers sequences of points on the real line which have been randomly translated, and provides conditions under which various notions of convergence to a limiting point process are equivalent. In particular we consider…

Number Theory · Mathematics 2024-08-15 Juan Arias de Reyna , Brad Rodgers

Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero.…