Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

Neighborhood and Efficiency in Manufacturing in Brazilian Regions: A Spatial Markov Chain Analysis

This paper analyzes the geography of regional competitiveness in manufacturing in Brazil. The authors estimate stochastic frontiers to calculate regional efficiency of representative firms in 137 regions in the period 2000-2006, in four sectors defined by technological intensity. The efficiency results are analyzed using Markov Spatial Transition Matrices to provide insights into the transition of regions between efficiency levels, considering their local spatial context. The results indicate that geography plays an important role in manufacturing competitiveness. In particular, regions with more competitive neighbors are more likely to improve their relative efficiency (pull effect) over time, and regions with less competitive neighbors are more likely to lose relative efficiency (drag effect). The authors find that the pull effect is stronger than the drag effect.

Characterization of the rat exploratory behavior in the elevated plus-maze with Markov chains

The elevated plus-maze is an animal model of anxiety used to study the effect of different drugs on the behavior of the animal It consists of a plus-shaped maze with two open and two closed arms elevated 50 cm from the floor The standard measures used to characterize exploratory behavior in the elevated plus-maze are the time spent and the number of entries in the open arms In this work we use Markov chains to characterize the exploratory behavior of the rat in the elevated plus-maze under three different conditions normal and under the effects of anxiogenic and anxiolytic drugs The spatial structure of the elevated plus-maze is divided into squares which are associated with states of a Markov chain By counting the frequencies of transitions between states during 5-min sessions in the elevated plus-maze we constructed stochastic matrices for the three conditions studied The stochastic matrices show specific patterns which correspond to the observed behaviors of the rat under the three different conditions For the control group the stochastic matrix shows a clear preference for places in the closed arms This preference is enhanced for the anxiogenic group For the anxiolytic group the stochastic matrix shows a pattern similar to a random walk Our results suggest that Markov chains can be used together with the standard measures to characterize the rat behavior in the elevated plus-maze (C) 2010 Elsevier B V All rights reserved

Association between micronuclei frequency in pollen mother cells of Tradescantia and mortality due to cancer and cardiovascular diseases: A preliminary study in Sao Jose dos Campos, Brazil

The present study was designed to explore the correlation between the frequency of micronuclei in Trad-MN, measured across 28 biomonitoring stations during the period comprised between 11 of May and 2 of October, 2006, and adjusted mortality rates due to cardiovascular, respiratory diseases and cancer in Sao Jose dos Campos, Brazil, an area with different sources of air pollution. For controlling purposes, mortality rate due to gastrointestinal diseases (an event less prone to be affected by air pollution) was also considered in the analysis. Spatial distribution of micronuclei frequency was determined using average interpolation. The association between health estimators and micronuclei frequency was determined by measures of Pearson`s correlation. Higher frequencies of micronuclei were detected in areas with high traffic and close to a petrochemical pole. Significant associations were detected between micronuclei frequency and adjusted mortality rate due to cardiovascular diseases (r = 0.841, p = 0.036) and cancer (r = 0.890, p = 0.018). The association between mortality due to chronic obstructive pulmonary diseases was positive but did not reach statistical significance (r = 0.640, p = 0.172), probably because of the small number of events. Gastrointestinal mortality did not exhibit significant association with micronuclei frequency. Because the small number of observations and the nature of an ecological study, the present findings must be considered with caution and considered as preliminary. Further studies, performed in different conditions of contamination and climate should be done before considering Trad-MN in the evaluation of human health risk imposed by air pollutants. (C) 2009 Elsevier Ltd. All rights reserved.

Similar Markov chains

enin et al. (2000) recently introduced the idea of similarity in the context of birth-death processes. This paper examines the extent to which their results can be extended to arbitrary Markov chains. It is proved that, under a variety of conditions, similar chains are strongly similar in a sense which is described, and it is shown that minimal chains are strongly similar if and only if the corresponding transition-rate matrices are strongly similar. A general framework is given for constructing families of strongly similar chains; it permits the construction of all such chains in the irreducible case.

Path integrals for continuous-time Markov chains

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

Sazonalidade e potencial energético da biomassa residual agrícola na região dos Campos Gerais do Paraná

RESUMO Teve-se por objetivo, neste trabalho, avaliar as disponibilidades sazonal e espacial da biomassa residual da colheita das principais culturas de grãos, na região dos Campos Gerais, PR, estimar o potencial teórico de produção de energia elétrica a partir desses resíduos, bem como identificar os municípios da região com maior potencial para instalação de termelétricas movidas a biomassa. Dados de produtividade de milho, soja, trigo, cevada, aveia branca e aveia preta foram obtidos, na Secretaria de Agricultura do Paraná, para as safras 2008/2009 e 2009/2010 e, a partir do índice e do calendário de colheitas, estimou-se a produção e sazonalidade da biomassa residual das culturas analisadas. Foram coletadas amostras de biomassa destas espécies e determinou-se o poder calorífico superior (PCS) e o potencial teórico de produção de energia elétrica a partir dos resíduos quantificados. Os Campos Gerais do Paraná produziram 3.862.130 (2008/2009) e 4.107.932 Mg ha−1 (2009/2010) de biomassa residual total com o cultivo das seis culturas. A disponibilidade de biomassa concentra-se em março e abril (aproximadamente 60%), sendo inexpressiva em dezembro, janeiro e entre junho e agosto. A biomassa residual da colheita de grãos apresentou PCS comparável ao de espécies florestais e potencial total de produção de energia de 3.932 (2008/2009) e 4.185 GWh ano−1 (2009/2010). Dos municípios analisados, Tibagi e Castro são os mais promissores para a instalação de termelétricas movidas a biomassa, por apresentarem maior produção e melhor distribuição sazonal dos resíduos.