ON THE LOCAL TIME OF A SEMI-STABLE PROCESS
Mots-clés :
Local time, entropy, stable subordinatorRésumé
In this paper we develop the note [2]. However, we use a different method based on a formula which was established by one of us in [3].Téléchargements
Références
- Bally V., "Approximation theorems for the local time of a Markov process", Stud. Cerc. Mat., n°38, (1986), pp. 139-147.
- Bencherif-Madani A., "Une nouvelle construction du temps local d'un processus semi-stable", C.R. Acad. Sci. Paris, t. 321, Série I, (1995), pp. 1509-1511.
- Bencherif-Madani A., "On geometric measure properties and the arithmetic of the range of a subordinator", Far East J. Math. Sci., vol.6, n°6, (1998), pp. 949-967.
- Dellacherie C. and Meyer P.A., "Probabilités et potentiel", Chap. XII to XVI, Hermann, (1986).
- Getoor R.K., "Another limit theorem for local time", Z. Wahrsch'theorie & Verw. Geb., n°34, (1976), pp. 1-10.
- Getoor R.K. and Millar P.W., "Some limit theorems for local time", Comp. Math., vol.25, n°2, (1972), pp. 123-134.
- Griego H.J., "Local time as a derivative of occupation limes", Ill. J. Math., n°11, (1967), pp. 54-63.
- Ito K. and Mc Kean H.P., "Diffusion processes and their sample paths", Springer-Verlag, (1974).
- Kingman J.F.C., "An intrinsic description of local time", J. London Math. Soc., vol.6, n°2, (1973), pp. 725-731.
- Pollard H., "The representation of as a Laplace transform", Bull. Amer. Math. Soc., n°52, (1946), pp.908-910.
- Stone C.J., "The set of zeros of a semi-stable process", Ill. J. Math., n°7, (1963), pp. 631-637.
- Taylor S.J. and Fristedt B., "Constructions of local time for a Markov process", Z. Wahrsch'theorie & Verw. Geb., n°62, (1983), pp. 73-112.
- Taylor S.J. and Wendel J.G., "The exact Hausdorff measure of the zero set of a stable process", Z. Wahrsch'theorie & Verw. Geb., n°62, (1983), pp. 73-112.
- Williams D., "Lévy's downcrossing theorem", Z. Wahrsch'theorie & Verw. Geb., 40, (1977), pp.157-158.
- Williams D., "Diffusions, Markov processes and martingales", vol. I, Wiley (1979).