Related papers: Subexponential lower bounds for $f$-ergodic Markov…
We consider a form of state-dependent drift condition for a general Markov chain, whereby the chain subsampled at some deterministic time satisfies a geometric Foster-Lyapunov condition. We present sufficient criteria for such a drift…
This paper consists of four parts. In the first part, we explain what eigenvalues we are interested in and show the difficulties of the study on the first (non-trivial) eigenvalue through examples. In the second part, we present some (dual)…
In this paper we study the ergodicity and the related semigroup property for a class of symmetric Markov jump processes associated with time changed symmetric $\alpha$-stable processes. For this purpose, explicit and sharp criteria for…
Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…
We are interested in the rate of convergence of a subordinate Markov process to its invariant measure. Given a subordinator and the corresponding Bernstein function (Laplace exponent) we characterize the convergence rate of the subordinate…
We study Markov processes conditioned so that their local time must grow slower than a prescribed function. Building upon recent work on Brownian motion with constrained local time in [5] and [33], we study transience and recurrence for a…
Let Y be an Ornstein-Uhlenbeck diffusion governed by a stationary and ergodic Markov jump process X: dY_t=a(X_t)Y_t dt+\sigma(X_t) dW_t, Y_0=y_0. Ergodicity conditions for Y have been obtained. Here we investigate the tail propriety of the…
In this paper, we study an approximation scheme for L\'evy processes with drift in terms of a representation that is akin to the celebrated Mehler formula for L\'evy-Ornstein-Uhlenbeck processes. The approximation scheme is based on a…
The aim of this article is to prove that diffusion processes in $\mathbb{R}^d$ with a drift can be approximated by suitable Markov chains on $n^{-1}\mathbb{Z}^d$. Moreover, we investigate sufficient conditions on the conductances which…
In this paper we find nonasymptotic exponential upper bounds for the deviation in the ergodic theorem for families of homogeneous Markov processes. We find some sufficient conditions for geometric ergodicity uniformly over a parametric…
For general absorbed Markov processes $(X_t)_{0\leq t<\tau_{\partial}}$ having a quasi-stationary distribution (QSD) $\pi$ and absorption time $\tau_{\partial}$, we introduce a Dobrushin-type criterion providing for exponential convergence…
We study the infinite-horizon average (ergodic) risk sensitive control problem for diffusion processes under a general structural hypothesis: there is a partition of state space into two subsets, where the controlled diffusion process…
We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the…
We study the ergodic property of a continuous-state branching process with immigration and competition. The exponential ergodicity in a weighted total variation distance is proved under natural assumptions. The main theorem applies to…
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…
A new approach is developed for evaluating the convergence rate for nonlinear Markov chains (MC) based on the recently developed spectral radius technique of markovian coupling for linear MC and the idea of small nonlinear perturbations of…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
For Markov chains and Markov processes exhibiting a form of stochastic monotonicity (larger states shift up transition probabilities in terms of stochastic dominance), stability and ergodicity results can be obtained using order-theoretic…
We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Edgeworth type expansions of third order for transition densities are proved. This is done for time horizons that converge to 0. For this purpose we…