In the commented paper, it was pointed out that a certain set of conditioned probability density functions P(1), P(2),…, is both necessary and sufficient to fully describe the state of any classical stochastic process. But the announced set of constraints that those functions are obliged to satisfy was incomplete. Here we elaborate the full set of constraining conditions on the P(n) functions, and in so doing we expose the non-Markovian generalization of the Chapman–Kolmogorov equation.

1.
D. T.
Gillespie
, “
Describing the state of a stochastic process
,”
Am. J. Phys.
66
,
533
536
(
1998
).
This content is only available via PDF.
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.