Approximations for interactive Markov chains in discrete and continuous time
Bibliographic Data
| ID | 7516274 |
|---|---|
| Authors | John P Lehoczky (Carnegie Mellon University, corresponding author) |
| Year | 1980 |
| Volume | 7 |
| Issue | 2 |
| Pages | 139-157 |
| Publication date | 1980-11-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | Journal of Mathematical Sociology (JOURNAL) |
| Journal identifiers | ISSN: 0022-250X • E-ISSN: 1545-5874 |
| Publisher | Taylor & Francis (PUBLISHER • GB) |
| DOI | 10.1080/0022250x.1980.9989904 |
| OpenAlex | W1985605431 |
| Language | EN |
| Citations received | 6 |
| References cited | 8 |
A class of models called interactive Markov chains is studied in both discrete and continuous time. These models were introduced by Conlisk and serve as a rich class for sociological modeling, because they allow for interactions among individuals. In discrete time, it is proved that the Markovian processes converge to a deterministic process almost surely as the population size becomes infinite. More importantly, the normalized process is shown to be asymptotically normal with specified mean vector and covariance matrix. In continuous time, the chain is shown to converge weakly to a diffusion process with specified drift and scale terms. The distributional results will allow for the construction of a likelihood function from interactive Markov chain data, so these results will be important for questions of statistical inference. An example from manpower planning is given which indicates the use of this theory in constructing and evaluating control policies for certain social systems
Balance equation · Class (philosophy · Continuous-time Markov chain · Covariance · Discrete phase-type distribution · Discrete time and continuous time · Markov chain · Markov model · Markov process · Markov property · Markov renewal process · Mathematical optimization · Statistics · Variable-order Markov model · Advanced Queuing Theory Analysis · Applied Mathematics · Artificial Intelligence · Complex Network Analysis Techniques · Computer Science · Mathematics · Opinion Dynamics and Social Influence
| Unique citing works | 6 |
|---|---|
| Citations per year | 0.14 |
| Citation span | 1983 - 2015 (33) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 6 |