Related papers: On Escape rate for subshift with Markov measure
Using path-integral methods, a formula is deduced for the noise-induced escape rate from an attracting fixed point across an unstable fixed point in one-dimensional maps. The calculation starts from the trace formula for the eigenvalues of…
We address the extreme value problem of a one-dimensional dynamical system approaching a fixed target while constrained to avoid a fixed set which can be thought of as a small hole. The presence of the latter influences the extremal index…
We calculate the spectrum of Lyapunov exponents for a point particle moving in a random array of fixed hard disk or hard sphere scatterers, i.e. the disordered Lorentz gas, in a generic nonequilibrium situation. In a large system which is…
Kramers escape rate in the overdamped systems with the power-law distribution is studied. By using the mean first passage time, we derive the escape rate for the power-law distribution and obtain the Kramers' infinite barrier escape rate in…
In this paper we introduce some recent progresses on the convergence rate in Wasserstein distance for empirical measures of Markov processes. For diffusion processes on compact manifolds possibly with reflecting or killing boundary…
In this paper, we give quantitative bounds on the $f$-total variation distance from convergence of an Harris recurrent Markov chain on an arbitrary under drift and minorisation conditions implying ergodicity at a sub-geometric rate. These…
We consider symmetric Markov chains on $\Bbb Z^d$ where we do {\bf not} assume that the conductance between two points must be zero if the points are far apart. Under a uniform second moment condition on the conductances, we obtain upper…
We consider continuous-time Markov chain on a finite state space X. We assume X can be clustered into several subsets such that the intra-transition rates within these subsets are of order $\mathcal{O}(\frac{1}{\epsilon})$ comparing to the…
A measure on a locally compact group is called spread out if one of its convolution powers is not singular with respect to Haar measure. Using Markov chain theory, we conduct a detailed analysis of random walks on homogeneous spaces with…
The convergence rate in Wasserstein distance is estimated for empirical measures of ergodic Markov processes, and the estimate can be sharp in some specific situations. The main result is applied to subordinations of typical models excluded…
We address the problem of estimating the mixing time of a Markov chain from a single trajectory of observations. Unlike most previous works which employed Hilbert space methods to estimate spectral gaps, we opt for an approach based on…
We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…
We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly…
This review paper provides an introduction of Markov chains and their convergence rates which is an important and interesting mathematical topic which also has important applications for very widely used Markov chain Monte Carlo (MCMC)…
In this paper we prove that the asymptotic rate of exponential loss of memory of a finite state hidden Markov model is bounded above by the difference of the first two Lyapunov exponents of a certain product of matrices. We also show that…
We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic…
The error exponent in lossy source coding characterizes the asymptotic decay rate of error probability with respect to blocklength. The Marton's error exponent provides the theoretically optimal bound on this rate. However, computation…
Let $(X, Y) = (X_n, Y_n)_{n \geq 1}$ be the output process generated by a hidden chain $Z = (Z_n)_{n \geq 1}$, where $Z$ is a finite state, aperiodic, time homogeneous, and irreducible Markov chain. Let $LC_n$ be the length of the longest…
We study a one-dimensional exclusion process with a fixed jump length $I \ge 1$ in which a particle may advance or retreat $I$ sites provided all intermediate sites are vacant, with hopping rates of Arrhenius type depending on the local…
Suppose we are given the free product $V$ of a finite family of finite or countable sets $(V_i)_{i\in\mathcal{I}}$ and probability measures on each $V_i$, which govern random walks on it. We consider a transient random walk on the free…