Related papers: Some Comments on the Stochastic Eulerian Tour Prob…
We consider the hydrodynamic origin of anomalous current fluctuations in a family of stochastic charged cellular automata. Using ballistic macroscopic fluctuation theory, we study both typical and large fluctuations of the charge current…
The main difficulty in studying numerical method for stochastic evolution equations (SEEs) lies in the treatment of the time discretization (J. Printems. [ESAIM Math. Model. Numer. Anal. (2001)]). Although fruitful results on numerical…
In {\em{Holm}, Proc. Roy. Soc. A 471 (2015)} stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics…
About thirty years ago we looked for "minimal assumptions" on the data which guarantee that solutions to the $\,2-D\,$ evolution Euler equations in a bounded domain are classical. Classical means here that all the derivatives appearing in…
We identify an issue in recent approaches to learning-based control that reformulate systems with uncertain dynamics using a stochastic differential equation. Specifically, we discuss the approximation that replaces a model with fixed but…
New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: Stochastic approximation replaces regression in the LSM algorithm; Explicit…
Strong existence and pathwise uniqueness of solutions with $L^{\infty}$-vorticity of 2D stochastic Euler equations is proved. The noise is multiplicative and involves first derivatives. A Lagrangian approach is implemented, where a…
We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…
The goal of these notes is to provide an introduction to rough partial differential equations. For this purpose, we will present the theory of rough paths to the extend as it is required. Applications to stochastic partial differential…
The authors consider stochastic aspects of the stabilization problem for two and three-dimensional Oseen equations with help of feedback control defined on a part of the fluid boundary. Stochastic issues arise when inevitable unpredictable…
We analyze a tour-uncrossing heuristic for the Travelling Salesperson Problem, showing that its worst-case approximation ratio is $\Omega(n)$ and its average-case approximation ratio is $\Omega(\sqrt{n})$ in expectation. We furthermore…
This paper deals with robust optimization applied to network flows. Two robust variants of the minimum-cost integer flow problem are considered. Thereby, uncertainty in problem formulation is limited to arc unit costs and expressed by a…
We develop a novel computational method for evaluating the extreme excursion probabilities arising from random initialization of nonlinear dynamical systems. The method uses excursion probability theory to formulate a sequence of Bayesian…
This work establishes a scaling limit theorem for the Stefan problem incorporating a mushy region, demonstrating that solutions to stochastic variants with turbulent transport terms converge to the solution to a deterministic partial…
The multi-path Traveling Salesman Problem with stochastic travel costs arises in hybrid vehicle routing applications designed for Smart City and City Logistics, where multiple paths exist between each pair of locations. Travel times along…
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle,…
The travel time tomography problem is a coefficient inverse problem for the eikonal equation. This problem has well known applications in seismic. The eikonal equation is considered here in the circular cylinder, where point sources run…
In this paper, we establish the existence of probabilistically strong, measure-valued solutions for the stochastic incompressible Navier--Stokes equations and prove their convergence, in the vanishing viscosity limit, to probabilistically…
This work addresses the optimal covariance control problem for stochastic discrete-time linear time-varying systems subject to chance constraints. Covariance steering is a stochastic control problem to steer the system state Gaussian…
A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a…