Related papers: Ergodic convergence rates of Markov processes--eig…
We present a practical and effective method for rigorously estimating quantities associated to top eigenvalues of transfer operators to very high precision. The method combines explicit error bounds of the Lagrange-Chebyshev approximation…
Extreme value functionals of stochastic processes are inverse functionals of the first passage time -- a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for…
Characterizing whether a Markov process of discrete random variables has an homogeneous continuous-time realization is a hard problem. In practice, this problem reduces to deciding when a given Markov matrix can be written as the…
This paper provides a general and abstract approach to approximate ergodic regimes of Markov and Feller processes. More precisely, we show that the recursive algorithm presented in Lamberton & Pages (2002) and based on simulation algorithms…
We study the ergodic properties of a two-dimensional self-gravitating system using molecular dynamics simulations. We apply three different tests for ergodicity: a direct method comparing the time average of a particle momentum and position…
We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation…
We first extend Calder\'on's transfer principle to weighted spaces, and then we apply our results to obtain some new weighted inequalities in ergodic theory and ergodic $H^1$ spaces.
In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
The dissertation describes ergodic properties of some stochastic dynamical systems generated by Markov chains with values in the state space which is a Polish space. The mathematical model describing the process of cell division is…
We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability…
The rate of quantum ergodicity is studied for three strongly chaotic (Anosov) systems. The quantal eigenfunctions on a compact Riemannian surface of genus g=2 and of two triangular billiards on a surface of constant negative curvature are…
Two model problems of an elastic wedge with an internal and edge crack are analyzed. The problem of an internal crack reduces to an order-4 vector Riemann-Hilbert problem whose matrix kernel entries are meromorphic functions and have…
Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously…
The recently established spectral Favard theorem for bounded banded matrices admitting a positive bidiagonal factorization is applied to a broader class of Markov chains with bounded banded transition matrices, extending beyond the…
We obtain pointwise ergodic theorems with rate under conditions expressed in terms of the convergence of series involving $\|\sum_{k=1} ^nf\circ \theta^k\|_2$, improving previous results. Then, using known results on martingale…
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…
For any measure preserving system $(X,\mathcal{B},\mu,T_1,\ldots,T_d),$ where we assume no commutativity on the transformations $T_i,$ $1\leq i\leq d,$ we study the pointwise convergence of multiple ergodic averages with iterates of…
In this paper, we first introduce and define several new information divergences in the space of transition matrices of finite Markov chains which measure the discrepancy between two Markov chains. These divergences offer natural…
In the present paper we investigate the $L_1$-weak ergodicity of nonhomogeneous discrete Markov processes with general state spaces. Note that the $L_1$-weak ergodicity is weaker than well-known weak ergodicity. We provide a necessary and…