We estimate the decay of correlations for some Markov maps on a countable states space. A necessary and suucient condition is given for the transfer operator to be quasi-compact on the space of locally Lipschitz functions. In the non quasi-compact case, the decay of correlations depends on the contribution to the transfer operator of the complementary of nitely many cylinders. Estimates are giv...

The objects studied in survival and event history analysis are stochastic phenomena developing over time. It is therefore natural to use the highly developed theory of stochastic processes. We argue that this theory should be used more in event history analysis. Some specific examples are treated: Markov chains, martingale-based counting processes, birth type processes, diffusion processes and ...

We consider density-dependent Markov chains converging, as the scale parameter K>0 goes to infinity, solution of an ODE admitting exponentially stable equilibrium point. provide a new strong approximation density by Gaussian process, based on construction Kurtz using Komlós–Major–Tusnády theorem. show that given any threshold ?(K)?1 greater than multiple log(K)/K, time error needs reach ?(K) is...

We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These also ensure existence and ergodicity of Q-process, process conditionned upon never being absorbed. The technique relies on coupling procedure that is related Harris recurrence (for Markov Chains). It applies general continuous-time continuous-space processe...

in this paper semi-markov models are used to forecast the triple dimensions of next earthquake occurrences. each earthquake can be investigated in three dimensions including temporal, spatial and magnitude. semi-markov models can be used for earthquake forecasting in each arbitrary area and each area can be divided into several zones. in semi-markov models each zone can be considered as a state...

A birth-death chain is a discrete-time Markov on the integers whose transition probabilities $p_{i,j}$ are non-zero if and only $|i-j|=1$. We consider chains birth $p_{i,i+1}$ form periodic sequence, so that $p_{i,i+1}=p_{i \mod m}$ for some $m$ $p_0,\ldots,p_{m-1}$. The trajectory $(X_n)_{n=0,1,\ldots}$ of such satisfies strong law large numbers central limit theorem. study effect reordering $...

This paper is motivated by examples from stochastic reaction network theory. The $Q$-matrix of a can be derived the graph, an edge-labelled directed graph encoding jump vectors associated continuous time Markov chain on invariant space $\mathbb{N}^d_0$. An open question how to decompose $\mathbb{N}^d_0$ into neutral, trapping, and escaping states, closed communicating classes, whether this done...

in order to determine the exact birth rate and also percent of birth - orders in all births in the province of west azerbaijan, all centres of birth registration in the province were asked to fill a questionnaire at the time of issuing identity document for children. in the questionnaire, parents were asked to mention the place of birth, sex and birth order of the children and also the occupati...

Poisson’s equation has a lot of applications in various areas, such as Markov decision theory, perturbation central limit theorems (CLTs), etc. Usually it is hard to derive the explicit expression solution for chain on an infinitely many state space. Here we will present computational framework both discrete-time chains (DTMCs) and continuous-time (CTMCs), by developing technique augmented trun...