On nonlinear expectations and Markov chains under model uncertainty

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...

Allais’s Theory of ‘‘Expectations’’ Under Uncertainty

Innovative Logistics Management under Uncertainty using Markov Model

This paper proposes an innovative uncertainty management using a stochastic model to formulate logistics network starting from order processing, purchasing, inventory management, transportation, and reverse logistics activities. As this activity chain fits well with Markov process, we exploit the very principle to represent not only the transition among various activities, but also the inherent...

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...

On nonlinear discrete-time systems driven by Markov chains

The behavior of a class of hybrid systems in discrete-time can be represented by nonlinear difference equations with a Markov input. The analysis of such a system usually starts by establishing the Markov property of the joint process formed by combining the system’s state and input. There are, however, no complete proofs of this property. This paper aims to address this problem by presenting a...