Markov Processes with Identical Bridges
| dc.creator | Fitzsimmons, P. J. | |
| dc.date | 1998-03-12 | |
| dc.date.accessioned | 2026-07-07T05:24:04Z | |
| dc.date.available | 2026-07-07T05:24:04Z | |
| dc.description | Let X and Y be time-homogeneous Markov processes with common state space E, and assume that the transition kernels of X and Y admit densities with respect to suitable reference measures. We show that if there is a time t>0 such that, for each x\in E, the conditional distribution of (X_s)_{0 < s < t}, given X_0 = x = X_t, coincides with the conditional distribution of (Y_s)_{0 < s < t}, given Y_0 = x = Y_t, then the infinitesimal generators of X and Y are related by [L^Y]f = ψ^{-1}[L^X](ψf)-λf, where ψis an eigenfunction of L^X with eigenvalue λ. Under an additional continuity hypothesis, the same conclusion obtains assuming merely that X and Y share a ``bridge'' law for one triple (x,t,y). Our work entends and clarifies a recent result of I. Benjamini and S. Lee. | |
| dc.description | 12 pages. See also http://math.ucsd.edu/~pfitz/preprints.html | |
| dc.identifier | https://arxiv.org/abs/math/9803049 | |
| dc.identifier | http://arxiv.org/abs/math/9803049 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76691 | |
| dc.subject | Probability | |
| dc.subject | 60J25 (Primary) 60J35 (Secondary) | |
| dc.title | Markov Processes with Identical Bridges | |
| dc.type | text |