Related papers: Wasserstein perturbations of Markovian transition …
The fact that a Markov diffusion semi-group on $\mathbb R^d$ contracts the $L^p$ Wasserstein distance, which has been extensively used to establish uniform-in-time stability estimates (e.g. with respect to numerical discretization errors),…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
In this work we study the long-time behavior for subcritical measure-valued branching processes with immigration on the space of tempered measures. Under some reasonable assumptions on the spatial motion, the branching and immigration…
We present a simple approach to study the one-dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of…
Perturbation theory for Markov chains addresses the question how small differences in the transitions of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the…
A formula for the transition density of a Markov process defined by an infinite-dimensional stochastic equation is given in terms of the Ornstein--Uhlenbeck bridge and a useful lower estimate on the density is provided. As a consequence,…
We introduce a unified framework to estimate the convergence of Markov chains to equilibrium in Wasserstein distance. The framework can provide convergence bounds with rates ranging from polynomial to exponential, all derived from a…
Several integrate-to-threshold models with differing temporal integration mechanisms have been proposed to describe the accumulation of sensory evidence to a prescribed level prior to motor response in perceptual decision-making tasks. An…
We study the Wasserstein gradient flow of semi-discrete energies in the space of probability measures, that is functionals depending on two measures-one being an absolutely continuous density and the other an atomic measure. These energies…
This article is a continuation of our first work \cite{chaudruraynal:frikha}. We here establish some new quantitative estimates for propagation of chaos of non-linear stochastic differential equations in the sense of McKean-Vlasov. We…
We investigate the concept of cylindrical Wiener process subordinated to a strictly $\alpha$-stable L\'evy process, with $\alpha\in\left(0,1\right)$, in an infinite dimensional, separable Hilbert space, and consider the related stochastic…
The role of the Wasserstein distance in the thermodynamic speed limit inequalities for Markov jump processes is investigated. We elucidate the nature of the Wasserstein distance in the thermodynamic speed limit inequality from three…
In this paper, we provide bounds in Wasserstein and total variation distances between the distributions of the successive iterates of two functional autoregressive processes with isotropic Gaussian noise of the form $Y_{k+1} =…
Non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels are considered. It is shown that their stability properties can be studied in terms of an associated class of piecewise deterministic Markov processes,…
We present a methodology for predictable and safe covariance steering control of uncertain nonlinear stochastic processes. The systems under consideration are subject to general uncertainties, which include unbounded random disturbances…
Markov decision processes (MDPs) are known to be sensitive to parameter specification. Distributionally robust MDPs alleviate this issue by allowing for \emph{ambiguity sets} which give a set of possible distributions over parameter sets.…
We establish subgeometric bounds on convergence rate of general Markov processes in the Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition and the existence of a "good" $d$-small set imply…
In this work we investigate the long-time behavior, that is the existence and characterization of invariant measures as well as convergence of transition probabilities, for Markov processes obtained as the unique mild solution to stochastic…
We examine the scaling limit of multi-period distributionally robust optimization (DRO) problems via a semigroup approach. Each period involves a worst-case maximization over distributions in a Wasserstein ball around the transition…
Markov decision process (MDP) is a decision making framework where a decision maker is interested in maximizing the expected discounted value of a stream of rewards received at future stages at various states which are visited according to…