Related papers: Subexponential upper and lower bounds in Wasserste…
We derive a relation between the dissipation in a stochastic dynamics and the Wasserstein distance. We show that the minimal amount of dissipation required to transform an initial state to a final state during a diffusion process is given…
Some microscopic dynamics are also macroscopically irreversible, dissipating energy and producing entropy. For many-particle systems interacting with deterministic thermostats, the rate of thermodynamic entropy dissipated to the environment…
We prove exponential convergence to the invariant measure, in the total variation norm, for solutions of SDEs driven by $\alpha$-stable noises in finite and in infinite dimensions. Two approaches are used. The first one is based on Harris…
Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
We establish upper bounds for the expected $p$-th power of the Gaussian-smoothed $p$-Wasserstein distance between a probability measure $\mu$ and the corresponding empirical measure $\mu_N$, whenever $\mu$ has finite $q$-th moment for some…
Via a Bismut-Elworthy-Li formula from [KPP23], we derive uniform gradient estimates for transition semigroups associated with stochastic differential equations driven by a large class of cylindrical L\'{e}vy processes which includes the…
Based on the explicit coupling property, the ergodicity and the exponential ergodicity of L\'{e}vy driven Ornstein-Uhlenbeck processes are established.
This paper establishes strong and weak convergence rates for slow-fast systems driven by $\alpha$-stable processes with jump coefficients. Unlike existing studies on multiscale systems driven by additive L\'{e}vy white noise, our model…
This paper establishes the quantitative stability of invariant measures $\mu_{\alpha}$ for $\mathbb{R}^d$-valued ergodic stochastic differential equations driven by rotationally invariant multiplicative $\alpha$-stable processes with…
In this paper, we study systems of $N$ interacting particles described by the classical and relativistic Langevin dynamics with singular forces and multiplicative noises. For the classical model, we prove the ergodicity, obtaining an…
We study the long time behaviour of a Markov process evolving in $\mathbb{N}$ and conditioned not to hit 0. Assuming that the process comes back quickly from infinity, we prove that the process admits a unique quasi-stationary distribution…
Finding the entropy rate of Hidden Markov Processes is an active research topic, of both theoretical and practical importance. A recently used approach is studying the asymptotic behavior of the entropy rate in various regimes. In this…
In this article, we establish Hoeffding's inequality for bounded Lipschitz functions of a class of not necessarily irreducible Markov models. The result complements the existing literature on this topic where Hoeffding's inequality for…
In this brief paper we find computable exponential convergence rates for a large class of stochastically ordered Markov processes. We extend the result of Lund, Meyn, and Tweedie (1996), who found exponential convergence rates for…
This article establishes cutoff stability also known as abrupt thermalization for generic multidimensional Hurwitz stable Ornstein-Uhlenbeck systems with (possibly degenerate) L\'evy noise at fixed noise intensity. The results are based on…
For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
We prove the convergence at an exponential rate towards the invariant probability measure for a class of solutions of stochastic differential equations with finite delay. This is done, in this non-Markovian setting, using the cluster…
Based on a variational expression for the steady-state entropy production rate in overdamped Langevin dynamics, we derive concrete upper bounds on the entropy production rate in various physical settings. For particles in a thermal…