Absolute continuity/singularity and relative entropy properties for probability measures induced by diffusions on infinite time intervals

A probabilistic approach to bounded/positive solutions for Schrödinger operators with certain classes of potentials

“…The role of φ here is played by |b| 2 in the proof of Theorem 3 in [3].) Thus, part (ii) now also follows from (1.2).…”

“…In order not to disrupt the exposition, we wait until the end of this section to explain how Theorem BA-P follows from [3].…”

“…It was also shown in [3] that for each function ψ as in part (ii) of the present theorem, it is possible to construct a function φ which satisfies the growth condition in part (ii) and is such that…”

“…2). Also, in the proof of Theorem 2 in [3], the limit appearing in the displayed formula between (3.3) and (3.4) should be outside of the expectation, and the statement in (3.4) should be in probability rather than almost surely. Then (3.7) there will hold for a sequence of times converging to infinity rather than for a continuum of times.…”

“…(See Theorem 3 in [3], in conjunction with Theorems 1 and 2 and Corollary 4 there. The role of φ here is played by |b| 2 in the proof of Theorem 3 in [3].)…”