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Kramers-Moyal master equation

For a jump process with rate

W (n, r)

from state

n

to

n + r

, probability balance gives

\partial_{t} P (n, t) = \sum_{r} [P (n - r, t) W (n - r, r) - P (n, t) W (n, r)] .

The first term is inflow from

n - r

and the second is outflow from

n

.

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