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Ito excursion theory via resolvents. (English) Zbl 0528.60073


MSC:

60J50 Boundary theory for Markov processes
60J45 Probabilistic potential theory
60J60 Diffusion processes

Citations:

Zbl 0089.138
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References:

[1] Feller, W., Generalised second order differential operators and their lateral conditions, Illinois J. Math., 1, 459-504 (1957) · Zbl 0077.29102
[2] Fristedt, B., Sample functions of stochastic processes with stationary independent increments, Advances in Probability 3 (1974), New York: Dekker, New York · Zbl 0309.60047
[3] Getoor, R. K., Markov Processes: Ray Processes and Right Processes, Lecture Notes in Mathematics 440 (1975), Berlin, Heidelberg, New York: Springer, Berlin, Heidelberg, New York · Zbl 0299.60051
[4] Getoor, R. K.; Sharpe, M. J., Last exit times and additive functionals, Ann. Probab., 1, 550-569 (1973) · Zbl 0324.60062
[5] Ikeda, N.; Watanabe, S., Stochastic Differential Equations and Diffusion Processes (1981), Amsterdam-Tokyo: North Holland-Kodansha, Amsterdam-Tokyo · Zbl 0495.60005
[6] Itô, K.: Poisson point processes attached to Markov processes. Proc. 6^th Berkeley Sympos. Math. Statist. Probab. Vol. 3, University of California Press, 225-240 (1971)
[7] Itô, K.; McKean, H. P., Brownian motion on a half line, Illinois J. Math., 7, 181-231 (1963) · Zbl 0114.33601
[8] Itô, K.; McKean, H. P., Diffusion Processes and their Sample Paths (1965), Berlin, Heidelberg, New York: Springer, Berlin, Heidelberg, New York · Zbl 0127.09503
[9] Jeulin, T., Un théorème de J.W. Pitman. Séminaire de Probabilités XIII, Lecture Noes in Mathematics 721, 521-532 (1979), Berlin, Heidelberg, New York: Springer, Berlin, Heidelberg, New York
[10] Neveu, J.: Entrance, exit and fictitious states for Markov chains. Proc. Aarhus Colloq. Combin. Probab. 64-68 (1962) · Zbl 0285.60052
[11] Pitman, J. W., One-dimensional Brownian motion and the three-dimensional Bessel process, J. Appl. Probab., 7, 511-526 (1975) · Zbl 0332.60055
[12] Reuter, G. E.H., Denumerable Markov Processes (II), J. London Math. Soc., 34, 81-91 (1959) · Zbl 0089.13803
[13] Rogers, L. C.G., Williams’ characterisation of the Brownian excursion law: proof and applications, Séminaire de Probabilités XV, 227-250 (1981), Berlin, Heidelberg, New York: Springer, Berlin, Heidelberg, New York · Zbl 0462.60078
[14] Rogers, L. C.G.; Pitman, J. W., Markov functions, Ann. Probab., 9, 573-582 (1981) · Zbl 0466.60070
[15] Walsh, J. B., A diffusion with a discontinuous local time, Temps locaux, Asterisque, 52-53, 37-45 (1978)
[16] Williams, D., Path decomposition and continuity of local time for one-dimensional diffusions, Proc. London Math. Soc. (3), 28, 738-768 (1974) · Zbl 0326.60093
[17] Williams, D., On Lévy’s downcrossing theorem, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 40, 157-158 (1977) · Zbl 0372.60115
[18] Williams, D., Diffusions, Markov Processes, and Martingales. Vol. I (1979), Chichester: Wiley, Chichester
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