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Journal of the London Mathematical Society 1985 s2-32(1):166-176; doi:10.1112/jlms/s2-32.1.166
© 1985 by London Mathematical Society
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© Oxford University Press

Recurrence of a Diffusion Process to a Shrinking Target

Peter Baxendale

Department of Mathematics, University of Aberdeen Aberdeen AB9 2TY

Let {Xt: t ≥ 0} be a non-degenerate diffusion process on a compact manifold M. A criterion is obtained for the recurrence of Xt to an open ball in M whose centre is fixed and whose radius is decreasing as t increases. A comparison is made between this criterion and a result due to Spitzer for 2-dimensional Brownian motion.


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