A note on Dirichlet processes

• Autorzy: Rozkosz A.
• Języki publikacji: EN

Abstrakty

EN

We consider an m-symmetric conservative Hunt process (Chi, Rho[chi]) on Chi such that for some phi [belongs to] L2(Chi; my) the composite process phi(Chi) is for quasi every starting point chi [belongs to] Chi a continuous Rho[chi]-Dirichlet process in the sense of Foellmer. We show that the martingale and the zero quadratic variation parts in the decomposition od phi(Chi} can be chosen to be additive functionals and moreover, how to pass from Foellmer's decomposition to Fukushima's and the Lyons-Zheng decompositions of phi(Chi).

Słowa kluczowe

EN

additive functional; Dirichlet process; Markov process

PL

funkcjonał addytywny; proces Dirichleta; proces Markowa; teoria prawdopodobieństwa

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 3
• Strony: 277--286
• Opis fizyczny: Bibliogr. 9 poz.,

Twórcy

autor

Rozkosz A.

• Faculty of Mathematics and Informatics, Nicholas Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

• [1] H. Föllmer, Dirichlet processes, in: Stochastic integrals (Durham 1980), ed.: D. Williams, Lecture Notes in Math., Springer, Berlin, 851 (1981) 476-478.
• [2] M. Fukushima, Y. Oshima, M. Takeda, Dirichlet forms and symmetric Markov processes, Walter de Gruyter, Berlin, New York 1994.
• [3] R. Sh. Liptser, A. N. Shiryayev, Theory of martingales, Kluwer, Dordrecht 1989.
• [4] T. J. Lyons, T. S. Zhang, Decomposition of Dirichlet processes and its application, Ann. Probab., 22 (1994) 494-524.
• [5] T. J. Lyons, W. A. Zheng, A crossing estimate for the canonical process on a Dirichlet space and a tightness result, in: Colloque Paul Lévy sur les processus stochastiques (Palaiseau 1987), Astérisque, 157--158 (1988) 249-271.
• [6] R. Rebolledo, La méthode des martingales apliguée à la convergence en loi des processus, Bull. Soc. Math. France, Memoire, 62 (1979) 1-125.
• [7] A. Rozkosz, On Dirichlet processes Associated with second order divergence form operators, Potential Anal., (2000), to be published.
• [8] A. Rozkosz, L. Słomiński, Extended convergence of Dirichlet processes, Stochastics Stochastics Rep., 65 (1998) 79-109.
• [9] A. Rozkosz, L. Słomiński, Stochastic representation of reflecting diffusions corresponding to divergence form operators, Studia Math., 139 (2000) 141-174.