Related papers: Iterated Logarithm Bounds of BGC Stochastic Proces…
This document is an informal bibliography of the papers dealing with distributed approximation algorithms. A classic setting for such algorithms is bounded degree graphs, but there is a whole set of techniques that have been developed for…
The dynamic Schr\"odinger bridge problem provides an appealing setting for solving constrained time-series data generation tasks posed as optimal transport problems. It consists of learning non-linear diffusion processes using efficient…
Graph generation is a critical yet challenging task, as empirical analyses require a deep understanding of complex, non-Euclidean structures. Diffusion models have recently made significant advances in graph generation, but these models are…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control…
The computational cost of the boundary-condition-enforced immersed boundary method (IBM) increases in the order of $\mathcal{O}(N^2)$ as the number of Lagrangian points, $N$, increases. This is due to the time-consuming calculation of the…
Deep neural networks suffer from poor generalization to unseen environments when the underlying data distribution is different from that in the training set. By learning minimum sufficient representations from training data, the information…
Consider the problem of learning the drift coefficient of a stochastic differential equation from a sample path. In this paper, we assume that the drift is parametrized by a high dimensional vector. We address the question of how long the…
In this note, we establish a compact law of the iterated logarithm under the upper capacity for independent and identically distributed random variables in a sub-linear expectation space. For showing the result, a self-normalized law of the…
An influential line of recent work has focused on the generalization properties of unregularized gradient-based learning procedures applied to separable linear classification with exponentially-tailed loss functions. The ability of such…
Recently, in the paper: T. Koszto{\l}owicz and A. Dutkiewicz, Phys. Rev. E \textbf{104}, 014118 (2021) the $g$--subdiffusion equation with fractional Caputo time derivative with respect to another function $g$ has been considered. This…
In this paper, we establish the law of the iterated logarithm for a wide class of non-stationary, continuous-time Markov processes evolving on Polish spaces. Specifically, our result applies to certain additive functionals of processes…
We consider the problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control. The system is stochastically driven through the control…
Matrix differential Riccati equations are central in filtering and optimal control theory. The purpose of this article is to develop a perturbation theory for a class of stochastic matrix Riccati diffusions. Diffusions of this type arise,…
In this paper, we propose a new framework to study distributed optimization problems with stochastic gradients by employing a multi-agent system with continuous-time dynamics. Here the goal of the agents is to cooperatively minimize the sum…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
This paper proposes and analyzes two new policy learning methods: regularized policy gradient (RPG) and iterative policy optimization (IPO), for a class of discounted linear-quadratic control (LQC) problems over an infinite time horizon…
We study the dynamics of a point particle in a periodic array of spherical scatterers, and construct a stochastic process that governs the time evolution for random initial data in the limit of low scatterer density (Boltzmann-Grad limit).…
We provide new, mild conditions for strict stationarity and ergodicity of a class of BEKK processes. By exploiting that the processes can be represented as multivariate stochastic recurrence equations, we characterize the tail behavior of…
We prove the dynamic programming principle for a class of diffusion processes controlled up to the time of exit from a cylindrical region $[0,T)\times G$. It is assumed that the functional to be maximized is in the Lagrange form with…