The multidimensional markov chain with prespecified asymptotic means,and (auto-)covariances

In this paper a method is presented to construct random time series which, starting from their present values, converge to stationary time series with a priori specified mean values, standard deviations, correlations and autocorrelations. The method is applied to simulate time series of price-inflation, wage-inflation, and interest rates, whose mean values, standard deviations, correlations and autocorrelations converge to the values which are estimated from historical data This application is a circular part of a Decision Support System which assists management of pension funds in analysing new methods of calculating pension premiums.     

The definition of tree-indexed Markov chains in random environment and their existence

This paper gives the definition of tree-indexed Markov chains in random environment with discrete state space, and then studies some equivalent theorems of tree-indexed Markov chains in random environment. Finally, we give the equivalence on tree-indexed Markov chains in Markov environment and double Markov chains indexed by a tree.     

The strong laws of large numbers for countable non homogeneous hidden Markov models

In this article, we are going to study the strong laws of large numbers for countable non homogeneous hidden Markov models. First, we introduce the notion of countable non homogeneous hidden Markov models. Then, we obtain some properties for those Markov models. Finally, we establish two strong laws of large numbers for countable non homogeneous hidden Markov models. As corollaries, we obtain some known results of strong laws of large numbers for finite non homogeneous Markov chains.     

Statistical inference for some Volterra population processes in a random environment

We study the problem of maximum-likelihood estimation in some random-environment population models, defined through nonlinear ltǒ stochastic differential equations. It is shown that a criticality parameter can be estimated consistently. The asymptotic behavior of the estimators is analyzed, and a goodness-of-fit test is proposed.     

Non‐Parametric Estimation of the Conditional Distribution of the Interjumping Times for Piecewise‐Deterministic Markov Processes

This paper presents a non‐parametric method for estimating the conditional density associated to the jump rate of a piecewise‐deterministic Markov process. In our framework, the estimation needs only one observation of the process within a long time interval. Our method relies on a generalization of Aalen's multiplicative intensity model. We prove the uniform consistency of our estimator, under some reasonable assumptions related to the primitive characteristics of the process. A simulation study illustrates the behaviour of our estimator.     

Case study in data analysis: Variables related to codling moth abundance and the efficacy of the Okanagan Sterile Insect Release Program

The authors consider the effect of orchard attributes and landscape in a heterogeneous area on the efficacy of a control program for the codling moth in apple orchards in British Columbia. The context is first presented, along with a set of questions of importance to the Okanagan Valley Sterile Insect Release program. Two groups of analysts then address a number of these issues using methods for spatial‐temporal data including counts, proportions and Bernoulli variables. The models are then compared and the relevance of the results to this operational program is discussed.