Integrals for continuous-time Markov chains.

P K Pollett

doi:10.1016/s0025-5564(02)00161-x

Home/Archive/PubMed

PubMed · 12591626

Integrals for continuous-time Markov chains.

P K Pollett

View original source ↗Export metadata ↓

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

Birth Rate Computer Simulation Disasters Epidemiologic Methods Markov Chains Mortality Poisson Distribution Time Factors Journal Article Research Support, Non-U.S. Gov't

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

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

PubMed2003

Interpreting time-series analyses for continuous-time biological models--measles as a case study.

An increasing number of recent studies involve the fitting of mechanistic models to ecological time-series. In some cases, it is necessary for these models to be discrete-time approximations of continuous-time processes. We test the validity of discretization in the case of measles, where time-series models have recently been developed to estimate ecological parameters directly from data. We find that a non-homogeneous contact function is necessary to capture the host-parasite interaction in a discrete-time model, even in the absence of heterogeneities due to spatial or age structure. We derive a mathematical relationship describing the expected departure from mass-action transmission in terms of the epidemiological parameters in the model, and identify conditions under which the discretization process may fail.

Birth Rate↗

PubMed2003

From the Center of Disease Control and Prevention. State-specific trends in US live births to women born outside the 50 states and the District of Columbia--United States, 1990 and 2000.

Explore the source record for details and available documents.

Birth Rate↗

PubMed2003

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↗