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References
Austin, D. G., R. M. Blumenthal, and R. V. Chacon: On continuity of transition functions. Duke math. J. 25, 533–542 (1958).
Blumenthal, R. M., and R. K. Getoor: Sample functions of stochastic processes with stationary independent increments. J. Math. Mech., 10, 493–516 (1961).
—, and H. P. McKean, Jr.: Markov processes with identical hitting distributions. Illinois J. Math. 6, 402–420 (1962).
- Additive functional of Markov processes in duality. To appear in Trans. Amer. math. Soc.
Bochner, S.: Harmonic analysis and the theory of probability. Berkeley and Los Angeles, Univ. of Calif. Press. 1955.
Boylan, E.S.: Local times for a class of Markov processes. Illinois J. Math. 8, 19–39 (1964).
Dynkin, E. B.: Theory of Markov processes (English translation) Englewood Cliffs, N.J., Prentice-Hall, 1961.
Getoor, R. K.: The asymptotic distribution of the number of zero free intervals of a stable process. Trans. Amer. math. Soc., 106, 127–138 (1963).
Hunt, G. A.: Markov processes and potentials I, II, and III. Illinois. J. Math., 1, 44–93, 316–369 (1957), and 2, 151–213 (1958).
Karlin, S., and J. McGregor: Classical diffusion processes and total positivity. Journ. Math. Anal. and Appl., 1, 163–183 (1960).
Lamperti, J.: An invariance principle in renewal theory. Ann. math. Statistics, 33, 685–696 (1962).
McKean, H. P., jr., and K. Ito: Diffusion theory, forthcoming book.
Meyer, P. A.: Fonctionelles multiplicatives et additives de Markov. Ann. Inst. Fourier, 12, 125–230 (1962).
Stone, C. J.: The set of zeros of a semi-stable process. Illinois Journ. Math., 7, 631–637 (1963).
šur, M. G.: Continuous additive functionals of a Markov process. Doklady Akad. Nauk. SSSR, n. Ser. 137, 800–803, (1961) (in Russian). Translated in Soviet Mathematics, 2, 365–368 (1961).
Trotter, H. F.: A property of Brownian motion paths. Illinois J. Math., 2, 425–433 (1958).
Volkonski, V. A.: Additive functionals of a Markov process. Trudy Moskovsk math. Obšč., 9, 143–189 (1960) (in Russian).
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This research was supported, in part, by the National Science Foundation, G-21205.
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Blumenthal, R.M., Getoor, R.K. Local times for Markov processes. Z. Wahrscheinlichkeitstheorie verw Gebiete 3, 50–74 (1964). https://doi.org/10.1007/BF00531683
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DOI: https://doi.org/10.1007/BF00531683