We give sufficient conditions for non-explosion and transience of the solution (xₜ, pₜ) (in dimensions ≥ 3) to a stochastic Newtonian system of the form cases dxₜ= pₜ \, dt , \\ dpₜ= -∂ V(xₜ) /∂ x \, dt - ∂ c(xₜ) / ∂ x \, dξₜ,cases where \ξₜ≥ 0 is a d-dimensional Lévy process, dξₜ is an Itô differential and c∈ C²(Rᵈ,Rᵈ), V∈ C²(Rᵈ,R) such that V≥ 0.
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Kolokoltsov et al. (2002) studied this question.
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