Abstract
We discuss the solutions of a Kramers-Moyal-expansion-type master equation for a discrete Poisson process, truncated at an arbitrary orderM. As was shown some time ago solutions withM=3, 7, 11 are in better agreement with the exact solution than the solution truncated atM=2. If a δ function is used as an initial condition, the solutions start to oscillate very rapidly with increasingM leading to a δ-function behaviour at the integer points for largeM. If, however, more smooth initial conditions are used, the rapid oscillations die out for increasingM and the solutions converge to interpolations of the exact solution.
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