|WikiProject Mathematics||(Rated Start-class, Low-importance)|
|WikiProject Statistics||(Rated Start-class, Low-importance)|
There should be a link to master equations http://en.wikipedia.org/wiki/Master_equation which is more specific than stochastic processes for this matter.
The theoretical ideas behind the algorithm appeared in W Feller (1940) (meaning that for true probabilistic solutions of Kolmogorov equations the time to the next-jump was exponentially distributed. See Theorem I on page 497). The resolution of the Poisson race between events was known to Kolmogorv (1931) and enters in Feller's work in the introduction. Hence, it was Feller the first to complete the picture althought he did not refer to sample-paths as Doob did. http://www.ams.org/journals/tran/1940-048-03/S0002-9947-1940-0002697-3/S0002-9947-1940-0002697-3.pdf
Doob makes reference to Feller 1940 in his paper.
Among the first computer implementations of the algorithm are: An Artificial Realization of a Simple "Birth-and-Death" Process Author(s): David G. Kendall Source: Journal of the Royal Statistical Society. Series B (Methodological), Vol. 12, No. 1 (1950), pp. 116-119 Published by: Blackwell Publishing for the Royal Statistical Society Stable URL: http://www.jstor.org/stable/2983837
No reference to Doob in Kendall's paper,
Stochastic Processes or the Statistics of Change Author(s): Maurice S. Bartlett Source: Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 2, No. 1 (Mar., 1953), pp. 44-64 Published by: Blackwell Publishing for the Royal Statistical Society Stable URL: http://www.jstor.org/stable/2985327
No reference to Doob in this paper.
as well as (see comment by Mr JC Gower on page 64 who explains details of the program in the Manchester computer) Measles Periodicity and Community Size Author(s): M. S. Bartlett Source: Journal of the Royal Statistical Society. Series A (General), Vol. 120, No. 1 (1957), pp. 48-70 Published by: Blackwell Publishing for the Royal Statistical Society Stable URL: http://www.jstor.org/stable/2342553
No reference to Doob either.
Kolmogorov 1931 paper, with mathematical derivation of the equations know to physicists as Master equations is: http://www.springerlink.com/content/v724507673277262/fulltext.pdf
I prefer the page keeper/author to add these information rather than editing the page.
- I've skimmed through Doob's paper "Topics in the theory of Markoff chains" (1942) and haven't found any mention of sample-paths. Any idea in which page he talks about that? --Ricardohz (talk) 22:46, 27 October 2016 (UTC)
- In Doob's paper "Stochastic processes depending on a continuous parameter" (1937) some continuity properties of stochastic processes are shown and paths (trajectories) are treated explicitly but no method for sampling is provided --Ricardohz (talk) 19:48, 31 October 2016 (UTC)
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