On hitting single points by a multidimensional diffusion
R. Dante DeBlassie · Stochastics and stochastics reports · 1998
Consider a diffusion process with uniformly positive definite diffusion matrix . Assuming is bounded and measurable, if x 0 is a continuity point of , then for dimensions d≥3 the diffusion does not hit {x 0} almost surely. This is false in dimension . We derive an integral test on the modulus of continuity of at x 0 that ensures {x 0} is polar for the diffusion when The test is shown to be sharp