Search PubMed⌕ Search

PubMed · 12591626

Integrals for continuous-time Markov chains.

Abstract

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.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

P K Pollett. 2003. Integrals for continuous-time Markov chains.. https://doi.org/10.1016/s0025-5564(02)00161-x

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

Moment closure and the stochastic logistic model.

The quasi-stationary distribution of the stochastic logistic model is studied in the parameter region where its body is approximately normal. Improved asymptotic approximations of its first three cumulants are derived. It is shown that the same results can be derived with the aid of the moment closure method. This indicates that the moment closure method leads to expressions for the cumulants that are asymptotic approximations of the cumulants of the quasi-stationary distribution.

Birth Rate↗

Seasonality of births is associated with seasonality of marriages in Malta.

This study was carried out to quantify secular trends in seasonal variation in births in Malta, a small Mediterranean country where the vast proportion of births occur in wedlock due to a predominantly Roman Catholic population. It also related such variations to seasonal variation in marriages. Annual seasonal peaks of marriages and births were analysed over the period 1950-1996 by X11 ARIMA. A significant peak in marriages (n = 111,932) in the third quarter of the year was found for almost the entire period under study. This was paralleled by a peak in births (n = 299,558) for the period 1970-1996, which lagged after the peak in marriages by 13-14 months. For the period 1994-1996, when monthly data for monthly pregnancies were available by pregnancy order, the peak in births was caused by first pregnancies only. Seasonal patterns in births occur almost universally due to cultural and/or biometeorological factors. The best known patterns include those of the southern United States, where births decline in April and May, and in northern Europe, where births peak in March and April. In Malta, the late summer peak in births appears to be due to a practical and planned approach by Maltese couples to contraceptive planning, probably influenced by the Roman Catholic ethos and social pressures, with unprotected intercourse occurring only after marriage. In Malta, birth control, albeit by so-called natural methods, was introduced in the 1960s. Prior to this period, births peaked towards the beginning/end of the year, and this may be the more natural seasonality of births in Malta.

Birth Rate↗