Markov Processes with Identical Bridges

dc.creatorFitzsimmons, P. J.
dc.date1998-03-12
dc.date.accessioned2026-07-07T05:24:04Z
dc.date.available2026-07-07T05:24:04Z
dc.descriptionLet 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.description12 pages. See also http://math.ucsd.edu/~pfitz/preprints.html
dc.identifierhttps://arxiv.org/abs/math/9803049
dc.identifierhttp://arxiv.org/abs/math/9803049
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76691
dc.subjectProbability
dc.subject60J25 (Primary) 60J35 (Secondary)
dc.titleMarkov Processes with Identical Bridges
dc.typetext

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