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arxiv: 1409.3112 · v2 · pith:3TRR2MAPnew · submitted 2014-09-10 · 🧮 math.PR

On h -transforms of one-dimensional diffusions stopped upon hitting zero

classification 🧮 math.PR
keywords transformszerohittingone-dimensionalstoppeduponavoidboundary
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For a one-dimensional diffusion on an interval for which 0 is the regular-reflecting left boundary, three kinds of conditionings to avoid zero are studied. The limit processes are $ h $-transforms of the process stopped upon hitting zero, where $ h $'s are the ground state, the scale function, and the renormalized zero-resolvent. Several properties of the $ h $-transforms are investigated.

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