Time change approach to generalized excursion measures, and its application to limit theorems

Journal of Theoretical Probability

Volumn 21, Issue 1, 2008, Pages 246-265

  Fitzsimmons, Patrick J ^a   Yano, Kouji ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

Bessel meander; Conditional limit theorems; It 's excursion measure; Random time change

Indexed keywords

EID: 38349123869     PISSN: 08949840     EISSN: 15729230     Source Type: Journal    
DOI: 10.1007/s10959-007-0108-8     Document Type: Article

References (24)

1. Biane, P., Yor, M.: Valeurs principales associées aux temps locaux browniens et processus stables symétriques. C.R. Acad. Sci. Paris Sér. I Math. 300(20), 695-698 (1985)
2. Biane, P., Yor, M.: Valeurs principales associées aux temps locaux browniens. Bull. Sci. Math. (2) 111(1), 23-101 (1987)
3. Bingham, N.H., Goldie, C.M., Teugels, J.L.: Regular variation. Encyclopedia of Mathematics and its Applications, vol. 27. Cambridge University Press, Cambridge (1989)
4. Blumenthal, R.M.: Excursions of Markov processes. Probability and Its Applications. Birkhäuser, Boston (1992)
5. Bolthausen, E.: On a functional central limit theorem for random walks conditioned to stay positive. Ann. Probab. 4(3), 480-485 (1976)
6. Elliott, J.: Eigenfunction expansions associated with singular differential operators. Trans. Am. Math. Soc. 78, 406-425 (1955)
7. Iglehart, D.L.: Functional central limit theorems for random walks conditioned to stay positive. Ann. Probab. 2, 608-619 (1974)
8. Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes, 2nd edn. North-Holland Mathematical Library, vol. 24. North-Holland, Amsterdam (1989)
9. Itô, K.: Poisson point processes attached to Markov processes. in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Univ. California, Berkeley, CA, 1970/1971, vol. III: Probability Theory, pp. 225-239 (1972)
10. Itô, K., McKean, H.P. Jr.: Diffusion processes and their sample paths. Die Grundlehren der mathematischen Wissenschaften, Band 125. Springer, Berlin (1974). Second printing, corrected
11. Jeulin, T.: Semi-martingales et grossissement d'une filtration. Lecture Notes in Mathematics, vol. 833. Springer, Berlin (1980)
12. Kasahara, Y.: Spectral theory of generalized second order differential operators and its applications to Markov processes. Jpn. J. Math. (N.S.) 1(1), 67-84 (1975/76)
13. Kasahara, Y., Watanabe, S.: Brownian representation of a class of Lévy processes and its application to occupation times of diffusion processes. Ill. J. Math. 50, 515-539 (2006)
14. Kotani, S.: Krein's strings with singular left boundary. Rep. Math. Phys. (2007, to appear)
15. Li, Z., Shiga, T., Tomisaki, M.: A conditional limit theorem for generalized diffusion processes. J. Math. Kyoto Univ. 43(3), 567-583 (2003)
16. Pitman, J., Yor, M.: A decomposition of Bessel bridges. Z. Wahrsch. Verw. Geb. 59(4), 425-457 (1982)
17. Pitman, J., Yor, M.: Decomposition at the maximum for excursions and bridges of one-dimensional diffusions. In: Itô's Stochastic Calculus and Probability Theory, pp. 293-310. Springer, Tokyo (1996)
18. Pitman, J.W., Yor, M.: Some divergent integrals of Brownian motion. Adv. Appl. Probab. (Suppl.), 109-116 (1986)
19. Revuz, D., Yor, M.: Continuous martingales and Brownian motion, 3rd edn. Grundlehren der Mathematischen Wissenschaften, vol. 293. Springer, Berlin (1999)
20. Stone, C.: Limit theorems for random walks, birth and death processes, and diffusion processes. Ill. J. Math. 7, 638-660 (1963)
21. Watanabe, S.: Generalized arc-sine laws for one-dimensional diffusion processes and random walks. In: Stochastic Analysis, Ithaca, NY, 1993. Proc. Sympos. Pure Math., vol. 57, pp. 157-172. Amer. Math. Soc., Providence (1995)
22. Williams, D.: Path decomposition and continuity of local time for one-dimensional diffusions, I. Proc. Lond. Math. Soc. (3) 28, 738-768 (1974)
23. Xue, X.X.: A zero-one law for integral functionals of the Bessel process. In: Séminaire de Probabilités, XXIV, 1988/89. Lecture Notes in Mathematics, vol. 1426, pp. 137-153. Springer, Berlin (1990)
24. Yano, K.: Excursion measure away from an exit boundary of one-dimensional diffusion processes. Publ. RIMS 42(3), 837-878 (2006)