Related papers: Coupling and Applications
We describe a new family of coupling designs, extending the basic principle of stratified randomization to experiments with continuous, constrained multivariate, text/image and other irregular treatment spaces. Our approach is to first…
We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…
In compact settings, the convergence rate of the empirical optimal transport cost to its population value is well understood for a wide class of spaces and cost functions. In unbounded settings, however, hitherto available results require…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
Markov chain Monte Carlo (MCMC) methods are often used in clustering since they guarantee asymptotically exact expectations in the infinite-time limit. In finite time, though, slow mixing often leads to poor performance. Modern computing…
This paper considers the optimal control of time varying continuous time Markov chains whose transition rates are themselves Markov processes. In one set of problems the solution of an ordinary differential equation is shown to determine…
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…
Lecture notes (in French) of a master 2 level course in applied mathematics. Contents: Part I. Markov chains on a countable space. 1. Examples 2. Summary of basic properties. 3. Spectral theory and speed of convergence. 4. Lyapunov…
We employ scoring functions, used in statistics for eliciting risk functionals, as cost functions in the Monge-Kantorovich (MK) optimal transport problem. This gives raise to a rich variety of novel asymmetric MK divergences, which subsume…
We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise…
Many applications in networked control require intermittent access of a controller to a system, as in event-triggered systems or information constrained control applications. Motivated by such applications and extending previous work on…
We prove exponential decay of pair correlations for 1D stationary point processes when spacings satisfy a Markov condition, geometric ergodicity, and a condition on exponential moments. The conditions are phrased for stationary sequences of…
Invariance principles are obtained for a Markov process on a half-line with continuous paths on the interior. The domains of attraction of the two different types of self-similar processes are investigated. Our approach is to establish…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
We introduce a class of continuous-state branching processes with immigration, predation and competition, which can be viewed as a combination of the classical Lotka-Volterra model and continuous-state branching processes with competition…
Lectures deal with the theory of electronic transport, in particular with the electrical conductivity, in systems dominated by strong electron-electron repulsion. The concept of charge stiffness is introduced to distinguish conductors and…
A point-to-point wireless communication system in which the transmitter is equipped with an energy harvesting device and a rechargeable battery, is studied. Both the energy and the data arrivals at the transmitter are modeled as Markov…
We study the convergence of an $N$-particle Markovian controlled system to the solution of a family of stochastic McKean-Vlasov control problems, either with a finite horizon or Schr\"odinger type cost functional. Specifically, under…
An aperiodic and irreducible Markov chain on a finite state space converges to its stationary distribution. When convergence to equilibrium is measured by total variation distance, there exists an optimal coupling and a maximal coupling…