Open Access
February 1997 Recurrence and transience of diffusions in a half-space
Srinivasan Balaji, Sundareswaran Ramasubramanian
Bernoulli 3(1): 97-119 (February 1997).


For non-degenerate diffusions in the half-space with oblique reflection, a dichotomy between recurrence and transience is established; convenient characterizations of recurrence and transience are given. Verifiable criteria for recurrence/transience are derived in terms of the generator and the boundary operator. Using these criteria, `real variables proofs' of some results due to Rogers, concerning reflecting Brownian motion in a half-plane, are obtained. The problem of transience down a side in the case of diffusions in the half-plane is dealt with. Positive recurrence of diffusions in half-space is also considered; it is shown that the hitting time of any open set has finite expectation if there is just one positive recurrent point.


Download Citation

Srinivasan Balaji. Sundareswaran Ramasubramanian. "Recurrence and transience of diffusions in a half-space." Bernoulli 3 (1) 97 - 119, February 1997.


Published: February 1997
First available in Project Euclid: 4 May 2007

zbMATH: 0882.60078
MathSciNet: MR1466547

Keywords: boundary operator , generator , Lyapunov

Rights: Copyright © 1997 Bernoulli Society for Mathematical Statistics and Probability

Vol.3 • No. 1 • February 1997
Back to Top