Related papers: A non-conservative Harris ergodic theorem
We study the long-time behaviour of the growth-fragmentation equation, a nonlocal linear evolution equation describing a wide range of phenomena in structured population dynamics. We show the existence of a spectral gap under conditions…
For general, almost surely absorbed Markov processes, we obtain necessary and sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the…
We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and…
We propose a simple criterion, inspired from the irreducible aperiodic Markov chains, to derive the exponential convergence of general positive semi-groups. When not checkable on the whole state space, it can be combined to the use of…
We prove a random Ruelle--Perron--Frobenius theorem and the existence of relative equilibrium states for a class of random open and closed interval maps, without imposing transitivity requirements, such as mixing and covering conditions,…
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…
For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…
We develop a novel stability theory for Sinkhorn semigroups based on Lyapunov techniques and quantitative contraction coefficients, and establish exponential convergence of Sinkhorn iterations on weighted Banach spaces. This…
We study the long-time behaviour of the first-moment semigroup of a non conservative piecewise deterministic measure-valued stochastic process with support on R 2 + driven by a deterministic flow between random jump times, with a transition…
We study the long-time behavior of an additive functional that takes into account the jumps of a symmetric Markov process. This process is assumed to be observed through a biased observation scheme that includes the survival to events of…
The stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V-norm contraction methods, associated to functionally weighted Banach spaces for…
The classical condition on the existence of uniformly exponentially consistent tests for testing the true density against the complement of its arbitrary neighborhood has been widely adopted in study of asymptotics of Bayesian nonparametric…
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…
A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence…
Let $M$ be a semifinite von Neumann algebra and $T$ a positive contraction on both $L^1(M)$ and $L^\infty(M)$. We consider ergodic averages along a random sparse subsequence determined by independent Bernoulli variables $(X_n)_{n\geq 1}$…
We obtain non-uniform Edgeworth expansions for several classes of weakly dependent (non-stationary) sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or…
We develop a general framework for studying ergodicity of order-preserving Markov semigroups. We establish natural and in a certain sense optimal conditions for existence and uniqueness of the invariant measure and exponential convergence…
Entropic optimal transport problems play an increasingly important role in machine learning and generative modelling. In contrast with optimal transport maps which often have limited applicability in high dimensions, Schrodinger bridges can…
Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which…
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,…