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Local time is a semi-martingale. (English) Zbl 0468.60070


MSC:

60J55 Local time and additive functionals
60G48 Generalizations of martingales
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References:

[1] Barlow, M.T.: On Brownian Local Time. In: Séminaire de Probabilités XV, p. 189–190, Lect. Notes in Math.850, Berlin-Heidelberg-New York: Springer 1981
[2] Chung, K.L., Durrett, R.: Downcrossings and local time. Z. Wahrscheinlichkeitstheorie Verw. Gebiete35, 147–149 (1976) · Zbl 0348.60111
[3] Fisk, D.L.: Quasi-martingales. Trans. Amer. Math. Soc.120, 369–389 (1965) · Zbl 0133.40303
[4] Hunt, G.: Martingales et Processus de Markov. Paris: Dunod 1966 · Zbl 0158.35802
[5] Knight, F.B.: Random walks and a sojourn density process of Brownian motion. Trans. Amer. Math. Soc.109, 56–86 (1963) · Zbl 0119.14604
[6] McKean, H.P.: Stochastic Integrals. New York: Academic Press 1969. · Zbl 0191.46603
[7] Ray, D.B.: Sojourn times of diffusion processes. Ill. J. Math. 7, 615–630 (1963) · Zbl 0118.13403
[8] Walsh, J.B.: Downcrossings and the Markov property of local time. In: Temps Locaux, Astérisque 52–53, pp. 89–115 (1978)
[9] Walsh, J.B.: Excursions and local time. In: Temps Locaux, Astérisque 52–53, pp. 159–192 (1978)
[10] Williams, D.: Lévy’s downcrossing theorem. Z. Wahrscheinlichkeitstheorie Verw. Gebiete40, 157–158 (1977) · Zbl 0372.60115
[11] Williams, D.: Conditional excursion theory. In: Séminaire de Probabilités XIII, pp. 490–494, Lect. Notes in Math.721, Berlin-Heidelberg-New York: Springer 1979
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