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References
Darling, D.A., Kac, M.: On occupation times for Markov processes. Trans. Amer. Math. Soc., 84, 444–458 (1957)
Doburusin, R.L.: Two limit theorems for the simplest random walk on a line. Uspehi Mat. Nauk. 10, 139–146 (1955) (English translation)
Getoor, R.K., Sharpe, M.J.: Conformal martingales. Invent. Math. 16, 271–308 (1972)
Itô, K., McKean Jr., H.P.: Diffusion processes and their sample paths. Berlin-Heidelberg-New York: Springer 1965
Kallianpur, G., Robbins, H.: Ergodic property of the Brownian motion process. Proc. Nat. Acad. 39, 525–533 (1953)
Karlin, S., McGregor, J.L.: Occupation time laws for birth and death processes. Proc. 4th Berkeley Sympos. Math. Statist. Probab. Univ. Calif. vol. 2, 249–272 (1960)
Kasahara, Y.: Spectral theory of generalized second order differential operators and its applications to Markov processes. Japan. J. Math. 1, 67–84 (1975)
Kasahara, Y.: Limit theorems of occupation times for Markov processes. Publ. RIMS, Kyoto Univ. 12, 801–818 (1977)
Knight, F.B.: A reduction of continuous square-integrable martingale to Brownian motion. Lecture notes in Math. 190, 19–31. Berlin-Heidelberg-New York: Springer 1971
Papanicolaou, G.C., Stroock, D., Varadhan, S.R.S.: Martingale approach to some limit theorems. Duke Univ. Mathematics series III, Statistical Mechanics and Dynamical systems, 1977
Skorokhod, A.V.: Limit theorems for stochastic processes. (English transl.) Theor. Probability Appl. 1, 261–290 (1956)
Stone, C.: Limit theorems for random walks, birth and death processes, and diffusion processes. Illinois J. Math. 7, 638–660 (1963)
Watanabe, S.: A limit theorem for sums of non-negative i.i.d. random variables with slowly varying tail probabilities. (To appear in Proc. 5th International Multivariate Analysis.)
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Kasahara, Y., Kotani, S. On limit processes for a class of additive functional of recurrent diffusion processes. Z. Wahrscheinlichkeitstheorie verw Gebiete 49, 133–153 (1979). https://doi.org/10.1007/BF00534253
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DOI: https://doi.org/10.1007/BF00534253