By means of a singular perturbation scheme and large deviation estimates we expand the Lyapunov exponent and rotation number in terms of the (small) noise intensity ε for all 2 × 2 systems dXₜ^ε = AXₜ^ε dt + √ ε ∑k = 1ʳ Bₖ Xₜ^ε ∘ dWₜᵏ for which A is complex diagonalizable. Examples are given.
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Pardoux et al. (1988) studied this question.
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