A Generalization of Khasminskii's Theorem on the Existence of Invariant Measures for Locally Integrable Drifts

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Global properties of invariant measures (2005, background): “It is a consequence of the proof of [ 6, Theorem 1.1 ] that AV belongs to L1().”
Steady States of Fokker–Planck Equations: I. Existence (2015, methodology): “Definition 2.1.”
Elliptic equations for invariant measures on finite and infinite dimensional manifolds (2001, background): “3 in [16] it follows that there existsμl ∈ P(M) with densitypl such thatpl = 0 onB l , pl ∈Hα,1(Bl;λM), and ∫ LZf dμl = 0, ∀f ∈C∞(M) with suppf ⊂ B l .”
On Parabolic Equations for Measures (2008, result): “In this respect, our approach is closer to that of [4], [5], [6] and [9] in the elliptic case.”
ON REGULARITY OF TRANSITION PROBABILITIES AND INVARIANT MEASURES OF SINGULAR DIFFUSIONS UNDER MINIMAL CONDITIONS (2001, background): “3) has been proved in [4] under the following conditions: A is locally uniformly nondegenerate, a 2 H p, 1 loc ðRÞ, b 2 LplocðR Þ, p > d, and there exists a positive function V 2 C(2)ðRd Þ such that VðxÞ ! þ1 and LA, bVðxÞ ! 1 as jxj ! þ1.”