Abstract
Let Pt be a submarkov semigroup on a Lusin topological state space E with Borel field E. We call a positive sigma-finite measure m on E an eigenmeasure if mPt = e-ct m for some real number c. We call a positive E-measurable function f an eigenfunction if ptf = e-ctf for some real number c. In each case, we call c the eigenvalue of either the eigenmeasure or the eigenfunction. Eigenmeasures are also known by the name quasi-stationary distributions in the Markov chain literature: see [5], [17], [18].
Research supported in part by NSF Grant DMS-83182204
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Glover, J. (1986). Quasi-Stationary Distributions, Eigenmeasures, and Eigenfunctions of Markov Processes. In: Çinlar, E., Chung, K.L., Getoor, R.K. (eds) Seminar on Stochastic Processes, 1984. Progress in Probability and Statistics, vol 9. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6745-1_5
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