For a probability density on the whole real line, if the density and its derivatives decay sufficiently fast that all boundary terms vanish, two integrations by parts give
(1)
while the diffusion term contributes zero to the first moment.

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  1. Diffusion approximation of a birth-death process
  2. Birth-death process
  3. Continuous-time Markov chain
  4. Markov chain
  5. Markov process
  6. Probability theory
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