Recombination Processes and Nonlinear Markov Chains

Recombination Processes and Nonlinear Markov Chains

Bacteria are known to exchange genetic information by horizontal gene transfer. Since the frequency of homologous recombination depends on the similarity between the recombining segments, several studies examined whether this could lead to the emergence of subspecies. Most of them simulated fixed-size Wright-Fisher populations, in which the genetic drift should be taken into account. Here, we u...

Markov Chains and Jump Processes

Markov Chains and De-initialising Processes

We define a notion of de-initialising Markov chains. We prove that to analyse convergence of Markov chains to stationarity, it suffices to analyse convergence of a deinitialising chain. Applications are given to Markov chain Monte Carlo algorithms and to convergence diagnostics.

Level-crossing Ordering of Semi-markov Processes and Markov Chains

We extend the definition of level-crossing ordering of stochastic processes, proposed by Irle andGani (2001), to the case in which the times to exceed levels are compared using an arbitrary stochastic order, and work, in particular, with integral stochastic orders closed for convolution. Using a sample-path approach, we establish level-crossing ordering results for the case in which the slower ...

Nonlinear Regression with Harris Recurrent Markov Chains

In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory for the proposed estimators. Our results show that the convergence rates for the estimators rely not only on the properties of the nonlinear regression func...