Timereversal of reflected Brownian motions in the orthant
Abstract
We determine the processes obtained from a large class of reflected Brownian motions (RBMs) in the nonnegative orthant by means of time reversal. The class of RBMs we deal with includes, but is not limited to, RBMs in the socalled HarrisonReiman class [4] having diagonal covariance matrices. For such RBMs our main result resolves the longstanding open problem of determining the time reversal of RBMs beyond the skewsymmetric case treated by R.J. Williams in [16]. In general, the timereversed process itself is no longer a RBM, but its distribution is absolutely continuous with respect to a certain auxiliary RBM. In the course of the proof we introduce a novel discrete approximation scheme for the class of RBMs described above, and use it to determine the semigroups dual to the semigroups of such RBMs.
 Publication:

arXiv eprints
 Pub Date:
 July 2013
 arXiv:
 arXiv:1307.4422
 Bibcode:
 2013arXiv1307.4422S
 Keywords:

 Mathematics  Probability;
 60H10;
 60F17;
 60G10;
 60J27
 EPrint:
 13 pages