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- W4242946543 abstract "In the study of dynamical systems perturbed by noise, it is important to know whether the stochastic process of interest has a stationary distribution. Four necessary and sufficient conditions are formulated for the existence of a finite invariant measure for a Feller process on a σ-compact metric (state) space. These conditions link together stability notions from several fields. The first uses a Lyapunov function reminiscent of Lagrange stability in differential equations; the second depends on Prokhorov's condition for sequential compactness of measures; the third is a recurrence condition on the ergodic averages of the transition operator; and the fourth is analogous to a condition of Ulam and Oxtoby for the nonstochastic case." @default.
- W4242946543 created "2022-05-12" @default.
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- W4242946543 date "1968-04-01" @default.
- W4242946543 modified "2023-10-18" @default.
- W4242946543 title "Finite regular invariant measures for Feller processes" @default.
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- W4242946543 doi "https://doi.org/10.2307/3212087" @default.
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