相关论文: The ODE method for stability of skip-free Markov c…

This paper investigates the mean square exponential stabilization problem for a class of coupled PDE-ODE systems with Markov jump parameters. The considered system consists of multiple coupled hyperbolic PDEs and a finite-dimensional ODE,…

Given a possibly discontinuous, bounded function $f:\mathbb{R}\mapsto\mathbb{R}$, we consider the set of generalized flows, obtained by assigning a probability measure on the set of Carath\'eodory solutions to the ODE ~$\dot x = f(x)$. The…

We develop a backstepping-based observer design for a class of ODE - continuum-PDE cascade systems, which can be viewed as the limit, of a finite collection of ODE - $2 \times 2$ hyperbolic systems, as the number of individual PDE system…

The focus of this work is on local stability of a class of nonlinear ordinary differential equations (ODE) that describe limits of empirical measures associated with finite-state weakly interacting N-particle systems. Local Lyapunov…

We give a development of the ODE method for the analysis of recursive algorithms described by a stochastic recursion. With variability modelled via an underlying Markov process, and under general assumptions, the following results are…

We study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For {\em finite} networks we establish stability and some steady-state moment bounds under natural…

We consider the Schr\"odinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely"…

Stream stochastic gradient descent (SGD) is a simple and efficient method for solving online optimization problems in operations research (OR), where data is generated by parameter-dependent Markov chains. Unlike traditional approaches…

We consider the dynamics of a linear stochastic approximation algorithm driven by Markovian noise, and derive finite-time bounds on the moments of the error, i.e., deviation of the output of the algorithm from the equilibrium point of an…

A single-server queuing model is considered with customers that have deadlines. If a customer's deadline elapses before service is offered, the customer abandons the system (customers do not abandon while being served). When the server…

Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary…

The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…

A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…

We study a system, where a random flow of customers is served by servers (called agents) invited on-demand. Each invited agent arrives into the system after a random time; after each service completion, an agent returns to the system or…

The osmotic equation of state for the athermal bond fluctuation model on the simple cubic lattice is obtained from extensive Monte Carlo simulations. For short macromolecules (chain length N=20) we study the influence of various choices for…

Continuous normalizing flows (CNFs) and diffusion models (DMs) generate high-quality data from a noise distribution. However, their sampling process demands multiple iterations to solve an ordinary differential equation (ODE) with high…

In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…

We study a simple rate control scheme for a multiclass queuing network for which customers are partitioned into distinct flows that are queued separately at each station. The control scheme discards customers that arrive to the network…

We analyze asymptotically a differential-difference equation, that arises in a Markov-modulated fluid model. Here there are N identical sources that turn "on" and "off", and when "on" they generate fluid at unit rate into a buffer, which…

This note introduces a piecewise-deterministic queueing (PDQ) model to study the stability of traffic queues in parallel-link transportation systems facing stochastic capacity fluctuations. The saturation rate (capacity) of the PDQ model…