For Markov processes with absorption, we provide general criteria ensuring the existence and exponential non-uniform convergence in weighted total variation norm to a quasi-stationary distribution. We also characterize subset of its domain attraction by an integrability condition, prove right eigenvector for semigroup process ergodicity Q-process. These results are applied one-dimensional multi-dimensional diffusion processes, pure jump continuous time reducible several communication...

This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned long time behavior different stochastic size processes when 0 is an absorbing point almost surely attained by process. The hitting this point, namely extinction time, can be large compared to physical fluctuate for amount before actually occurs. phenomenon understood quasi-limiting distributions. In paper, general results...

In this note, we recall the definition of binary branching model with Moran type interactions (BBMMI) introduced in [8]. interacting particle system, particles evolve, reproduce and die independently and, a probability that may depend on configuration whole death trigger reproduction another particle, while event particle. We its relation to Feynman-Kac semigroup underlying Markov evolution improve L 2 distance between their normalisations proved [8], when additional regularity is assumed process.

We consider a strong Markov process with killing and prove an approximation method for the distribution of conditioned not to be killed when it is observed. The based on Fleming−Viot type particle system rebirths, whose particles evolve as independent copies original jump onto each others instead being killed. Our only assumption that number rebirths doesn't explode in finite time almost surely survival probability remains positive time. generalizes previous results comes speed convergence....

The first aim of the present note is to quantify speed convergence a conditioned process toward its $Q$-process under suitable assumptions on quasi-stationary distribution process. Conversely, we prove that, if converges uniformly conservative Markov which itself ergodic, then it admits unique and exponentially fast, in initial distribution. As an application, provide conditional ergodic theorem.

We study the existence and exponential ergodicity of a general interacting particle system, whose components are driven by independent diffusion processes with values in an open subset $\mathds{R}^d$, $d\geq 1$. The interaction occurs when hits boundary: it jumps to position chosen respect probability measure depending on whole system. Then we behavior such system number particles goes infinity. This leads us approximation method for Yaglom limit multi-dimensional unbounded drift defined...

We study the long-time behaviour of a Markov process evolving in N and conditioned not to hit 0. Assuming that comes back quickly from ∞, we prove admits unique quasistationary distribution (in particular, limit when time goes ∞). Moreover, converges exponentially fast total variation norm its provide bound for rate convergence. As first application our result, bring new insight on speed convergence birth-and-death processes: starting any initial conditional probability law ρ supported * if...

Abstract In this paper we study the quasi-stationary behavior of absorbed one-dimensional diffusions. We obtain necessary and sufficient conditions for exponential convergence to a unique distribution in total variation, uniformly with respect initial distribution. An important tool is provided by strict local martingale diffusions coming down from infinity. prove, under mild assumptions, that their expectation at any positive time bounded position. provide several examples extensions,...

In a first part, we prove Lyapunov-type criterion for the $\xi_1$-positive recurrence of absorbed birth and death processes provide new results on domain attraction minimal quasi-stationary distribution. second study ergodicity convergence Fleming-Viot type particle system whose particles evolve independently as process jump each others when they hit 0. Our main result is that sequence empirical stationary distributions converges to distribution process.

Our main result is to prove almost-sure convergence of a stochastic-approximation algorithm defined on the space measures noncompact space. motivation apply this measure-valued Pólya processes (MVPPs, also known as infinitely-many urns). idea use Foster–Lyapunov type criteria in novel way generalize methods Markov with underlying space, overcoming fairly general context one major difficulties existing studies subject. From MVPPs point view, our implies large class MVPPs; was only obtained...

The goal of this note is to show how recent results on the theory quasi-stationary distributions allow us deduce general criteria for geometric convergence normalized unbounded semigroups.

This article studies the quasi-stationary behaviour of absorbed onedimensional diffusion processes with killing on [0, ∞).We obtain criteria for exponential convergence to a unique distribution in total variation, uniformly respect initial distribution.Our approach is based probabilistic and coupling methods, contrary classical spectral theory results.Our general apply case where ∞ entrance 0 either regular or exit, are proved be satisfied under several explicit assumptions expressed only...

For Markov processes with absorption, we provide general criteria ensuring the existence and exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize subset of its domain attraction by an integrability condition, prove right eigenvector for semigroup process ergodicity Q-process. These results are applied one-dimensional multi-dimensional diffusion processes, pure jump continuous time reducible several communication classes,...

We provide a general criterion ensuring the exponential contraction of Feynman–Kac semi-groups penalized processes. This applies to time-inhomogeneous Markov processes with absorption and killing through penalization. also give asymptotic behavior expected penalization results convergence in total variation process up infinite time. For bounded penalization, converse result is obtained, showing that our sharp this case. Several cases are studied: we first show how can be simply checked for...

Mean telomere length in human leukocyte DNA samples reflects the different lengths of telomeres at ends 23 chromosomes and an admixture cells. However, only rudimentary information is available regarding distribution all cell types samples. Understanding configuration (LTLD) could be helpful capturing intrinsic elements that are not provided by mean (mLTL). The objective this study was to analyse LTLD its temporal variation adults. Leukocyte were donated on two occasions (8 years apart) 72...

We consider an elliptic and time-inhomogeneous diffusion process with time-periodic coefficients evolving in a bounded domain of $\mathbb{R}^d$ smooth boundary. The is killed when it hits the boundary (hard killing) or after exponential time (soft associated some rate function. branching particle interpretation non absorbed again behaves as set interacting particles absorbing medium. Between absorption times, evolve independently one from each other according to semigroup; absorbed, another...

This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death catastrophes multi-dimensional processes, modeling biological populations in interaction. To handle this situation, we develop original non-linear Lyapunov criteria. We obtain exponential convergence total variation conditional distributions to a unique distribution, uniformly respect initial distribution. Our results cover all which come down...

In this paper, we prove convergence and fluctuation results for measure-valued Pólya processes (MVPPs, also known as urns with infinitely-many colours). Our hold almost surely in L2. are the first second-order literature on MVPPs; they generalise classical from finitely-many-colour urns. As case, order shape of fluctuations depend whether "spectral gap is small or large". To these results, show that MVPPs stochastic approximations taking values set measures a measurable space E (the colour...