dX^ε = b(X^ε(t))dt + √ε dB(t)

is studied and the asymptotic behaviour in ε is investigated. The leading order term is obtained exactly and it is shown that at an equilibrium point there are only two possible forms for this term - Lévy or Hawkes—Truman. We also compute the next to leading order term and demonstrate the remarkable fact that it is identically zero.

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