In this paper, we introduce a new threshold model with poisson innovation: Threshold Integer-Valued Moving Average model (TINMA). We derive the numerical characteristics of TINMA(1) model. Stationary and ergodicity are also obtained. The methods of estimation under analysis is Yule-Walker. Some simulation results illustrate the performance of the proposed method.

In this paper it is shown that one can estimate the sum of the weights used to form a stationary moving average stochastic process based on nonnegative random variables by taking the limit in probability of suitable quotients, even when the random variables involved have infinite expectation.

Bounded parameter Markov Decision Processes (BMDPs) address the issue of dealing with uncertainty in the parameters of a Markov Decision Process (MDP). Unlike the case of an MDP, the notion of an optimal policy for a BMDP is not entirely straightforward. We consider two notions of optimality based on optimistic and pessimistic criteria. These have been analyzed for discounted BMDPs. Here we pro...

A Bayesian model selection for modelling a time series by an autoregressive–moving–average model (ARMA) is presented. The posterior distribution of unknown parameters and the selected orders are obtained by the Markov chain Monte Carlo (MCMC) method. An MCMC algorithm that represents the parameters of the model as a point process has been implemented. The method is illustrated on simulated seri...

As the same framework of Fuzzy decision processes with the discounted case we will specify an average fuzzy criterion model and develop its optimization by “fuzzy max order” under appropriate conditions. The average reward is characterized, by introducing a relative value function, as a unique solution of the associated equation. Also we derive the optimality equation using the “vanishing disco...

This paper presents sufficient conditions for the existence of stationary optimal policies for averagecost Markov Decision Processes with Borel state and action sets and with weakly continuous transition probabilities. The one-step cost functions may be unbounded, and action sets may be noncompact. The main contributions of this paper are: (i) general sufficient conditions for the existence of ...

Often the least appropriate assumption in traditional control charting technology is that process data constitute a random sample. In reality most process data are correlated—either temporally, spatially, or due to nested sources of variation. One approach to monitoring temporally correlated data uses a control chart on the forecast errors from a time series model of the process with, possibly,...

The harmonizable Piranashvili – type stochastic processes are approximated by a finite time shifted average sampling sum. Truncation error upper bound is established; various consequences and special cases are discussed. MSC(2000): 42C15, 60G12, 94A20.

We consider Markov decision processes (MDPs) with multiple long-run average objectives. Such MDPs occur in design problems where one wishes to simultaneously optimize several criteria, for example, latency and power. The possible trade-offs between the different objectives are characterized by the Pareto curve. We show that every Pareto optimal point can be ε-approximated by a memoryless strate...

P We investigate the problem of minimizing the Average-Value-at-Risk (AV aRτ ) of the discounted cost over a finite and an infinite horizon which is generated by a Markov Decision Process (MDP). We show that this problem can be reduced to an ordinary MDP with extended state space and give conditions under which an optimal policy exists. We also give a time-consistent interpretation of the AV aR...