Convergence of Averaged Occupation Times
Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 49-56

Voir la notice de l'article provenant de la source Cambridge University Press

Let X = {Xt, t ≥ 0} be a stationary Markov process with values in a measurable space (S, B), transition function p, and initial distribution concentrated at a point x ∊ S. The occupation times of a set A ∊ B are defined for t ≥ 0 by where 1A is the indicator function of A. The expected occupation times are given by
Lamb✝, Charles W. Convergence of Averaged Occupation Times. Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 49-56. doi: 10.4153/CMB-1975-010-5
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[1] 1. Breiman, L., Probability (Addison-Wesley, Reading 1968). Google Scholar

[2] 2. Brosamler, G. A., The asymptotic behavior of certain additive junctionals of Brownian motion, Inventiones Math., 20 (1973), 87-96. Google Scholar

[3] 3. Chung, K. L. and Erdös, P., Probability limit theorems assuming only the first moment I, Memoirs of the Amer. Math. Sac., 6 (1951). Google Scholar

[4] 4. Darling, D. A. and Kac, M., On occupation times for Markov processes, Trans. Amer. Math. Soc. 84 (1957), 444-458. Google Scholar

[5] 5. Feller, W., An introduction to probability theory and its applications, Volume II (Wiley, New York, 1971). Google Scholar

[6] 6. Kallianpur, G. and Robbins, H., Ergodic property of the Brownian motion process, Proc. Nat. Acad. Sci. U.S.A., 39 (1953), 525-533. Google Scholar

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