Some asymptotic laws for crossings and excursions
Colloque Paul Lévy sur les processus stochastiques (22-26 juin 1987. École Polytechnique, Palaiseau), Astérisque, no. 157-158 (1988), pp. 59-74.

Voir la notice du chapitre de livre provenant de la source Numdam

@incollection{AST_1988__157-158__59_0,
     author = {Burdzy, Krzysztof and Pitman, Jim W. and Yor, Marc},
     title = {Some asymptotic laws for crossings and excursions},
     booktitle = {Colloque Paul L\'evy sur les processus stochastiques (22-26 juin 1987. \'Ecole Polytechnique, Palaiseau)},
     series = {Ast\'erisque},
     pages = {59--74},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {157-158},
     year = {1988},
     zbl = {0666.60070},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AST_1988__157-158__59_0/}
}
TY  - CHAP
AU  - Burdzy, Krzysztof
AU  - Pitman, Jim W.
AU  - Yor, Marc
TI  - Some asymptotic laws for crossings and excursions
BT  - Colloque Paul Lévy sur les processus stochastiques (22-26 juin 1987. École Polytechnique, Palaiseau)
AU  - Collectif
T3  - Astérisque
PY  - 1988
SP  - 59
EP  - 74
IS  - 157-158
PB  - Société mathématique de France
UR  - http://geodesic.mathdoc.fr/item/AST_1988__157-158__59_0/
LA  - en
ID  - AST_1988__157-158__59_0
ER  - 
%0 Book Section
%A Burdzy, Krzysztof
%A Pitman, Jim W.
%A Yor, Marc
%T Some asymptotic laws for crossings and excursions
%B Colloque Paul Lévy sur les processus stochastiques (22-26 juin 1987. École Polytechnique, Palaiseau)
%A Collectif
%S Astérisque
%D 1988
%P 59-74
%N 157-158
%I Société mathématique de France
%U http://geodesic.mathdoc.fr/item/AST_1988__157-158__59_0/
%G en
%F AST_1988__157-158__59_0
Burdzy, Krzysztof; Pitman, Jim W.; Yor, Marc. Some asymptotic laws for crossings and excursions, dans Colloque Paul Lévy sur les processus stochastiques (22-26 juin 1987. École Polytechnique, Palaiseau), Astérisque, no. 157-158 (1988), pp. 59-74. http://geodesic.mathdoc.fr/item/AST_1988__157-158__59_0/

Azema, J., Duflo, M. and Revuz, D. (1967). Mesure invariante sur les classes récurrentes des processus de Markov. Z. Wahrscheinlichkeitstheorie 8, 157-181. | Zbl | DOI

Azema, J., Duflo, M. and Revuz, D. (1969). Propriétés relatives des processus de Markov récurrents. Z. Wahrscheinlichkeitstheorie 13, 286-314. | Zbl | DOI

Bingham, N. H. (1971). Limit theorems for occupation times of Markov processes. Z. Wahrscheinlichkeitstheorie 17, 1-22. | Zbl | DOI

Blumenthal, R. M. and Getoor, R. K. (1968). Markov processes and potential theory. Academic Press. | Zbl

Burdzy, K., Pitman, J. and Yor, M. (1987) Some asymptotic laws for crossings and excursions. Technical Report No. 112. Dept. Statistics, U. C. Berkeley.

Chung, K. L. (1973). Probabilistic approach in potential theory to the equilibrium problem. Ann. Inst. Fourier, Grenoble. 23, 3, 313-322 | EuDML | Zbl | mathdoc-id | DOI

Cohn, H. (1967). Conformal mapping on Riemann surfaces. Dover, New York. | Zbl

Darling, D. A. and Kac, M. (1957). Occupation times for Markov processes. Trans. Amer. Math. Soc. 84, 444-458. | Zbl | DOI

Fitzsimmons, P. J. (1987). On the excursions of Markov processes in classical duality. Prob. Rel. Fields 15, 159-178 | Zbl | DOI

Geman, D. and Horowitz, J. (1973). Remarks on Palm measures. Ann. Inst. Henri Poincaré Sec B, IX 213-232. | Zbl | mathdoc-id

Getoor, R. K. and Sharpe, M. J. (1973). Last exit decompositions and distributions. Indiana Univ. Math. J. 23, 377-404. | Zbl | DOI

Getoor, R. K. and Sharpe, M. J. (1982). Excursions of Dual processes. Adv. in Math. 45, 259-309 | Zbl | DOI

Getoor, R. K. and Steffens, J. (1986). Capacity theory without duality. Prob. Rel Fields 73, 3 415-446 | Zbl | DOI

Greenwood, P. and Pitman, J. W. (1980a). Construction of local time and Poisson point processes from nested arrays. J. London Math. Soc. (2) 22, 182-192. | Zbl | DOI

Itô, K. (1970). Poisson point processes attached to Markov processes. Proc. Sixth Berkeley Symp. Math. Statist. Prob. pp. 225-239. Univ. of California Press, Berkeley. | Zbl

Itô, K. and Mckean, H. P. (1965). Diffusion Processes and Their Sample Paths. Springer, Berlin. | Zbl

Kallianpur and Robbins (1953). Ergodic property of the Brownian motion process. Proc. Nat. Acad. Sci. U.S.A. 39, 525-533. | Zbl | DOI

Kasahara, Y. (1977). Limit theorems of occupation times for Markov processes. Publ. Res. Inst. Math. Sci. Kyoto 12, 801-808. | Zbl | DOI

Kasahara, Y. (1982). A Limit Theorem for Slowly Increasing Occupation Times. Ann. Prob. 10, 728-736. | Zbl | DOI

Kasahara, Y. and Kotani, S. (1979). On Limit Processes for a Class of Additive Functionals of Recurrent Diffusion Processes. Z. Wahrscheinlichkeitstheorie 49, 133-153. | Zbl | DOI

Kaspi, H. (1984). On invariant measures and dual excursions of Markov processes. Z. Wahrscheinlichkeitstheorie 66, 185-204. | Zbl | DOI

Kaspi, H. (1985). Excursion laws for Markov processes in classical duality. Ann. Prob. 13, 492-518. | Zbl | DOI

Kellogg, O. D. (1929). Foundations of potential theory. Springer, Berlin. | JFM | EuDML | DOI

Le Gall J. F. and Yor M. (1986). Etude asymptotique de certains mouvements browniens complexes avec drift. Probability and Related Fields, 71, 183-229 | Zbl | DOI

Lyons, T. and Mckean, H. P. (1984). Windings of the plane Brownian motion. Adv. in Math. 51, 212-225. | Zbl | DOI

Maisonneuve, B. (1975). Exit systems. Ann. Prob. 3, 399-411. | Zbl | DOI

Maruyama, G. and Tanaka, H. (1959). Ergodic property of N-dimensional recurrent Markov processes. Memoirs of Fac. Science, Kyushu Univ. Ser. A 13, 157-172. | Zbl

Mckean, H. P. (1965). A probabilistic interpretation of equilibrium charge distributions. J. Math. Kyoto Univ. 4, 617-625. | Zbl | DOI

Mitro, J. B. (1984). Exit systems for dual Markov processes. Z. Wahrscheinlichkeitstheorie 66, 259-267. | Zbl | DOI

Morse, P. M. and Feshbach, H. (1953). Methods of Theoretical Physics. Vol. 2. McGraw Hill. | Zbl

Mountford, T. (1987). The asymptotic distribution of the number of crossings between tangential circles by planar Brownian motion. Preprint. | Zbl

Neveu, J. (1968). Sur la structure des processus ponctuels stationnaires. C. R. Acad. Sci, t 267, A p. 561. | Zbl

Neveu, J. (1976). Sur les mesures de Palm de deux processus ponctuels stationnaires. Z. Wahrscheinlichkeitstheorie verw. Geb. 34, 199-203. | Zbl | DOI

Neveu, J. (1977). Processus ponctuels. Ecole d'Eté de Probabilités de Saint-Flour VI-1976. 250-446. Lecture Notes in Math. 598. Springer. | Zbl

Pitman, J. W. (1987). Stationary Excursions. Séminaire de Probabilités XXI, 289-302. Lecture Notes in Math. 1247. Springer-Verlag, Berlin. | Zbl | EuDML | mathdoc-id | DOI

Pitman, J. and Yor, M. (1986a). Asymptotic laws of planar Brownian motion. Ann. Prob. 14, 733-779. | Zbl | DOI

Pitman, J. W. and Yor, M. (1986b). Level crossings of a Cauchy process. Ann. Prob. 14, 780-792. | Zbl | DOI

Pitman, J. and Yor, M. (1986c). Some Divergent Integrals of Brownian Motion. Analytic and Geometric Stochastics : Supplement to Adv. Appl. Prob., Applied Prob. Trust, 109-116. | Zbl

Pitman, J. W. and Yor, M. (1987). Further asymptotic laws of planar Brownian motion. Technical Report No. 78, Dept. Statistics, U. C. Berkeley. To appear in Ann. Prob. | Zbl

Revuz, D. (1975). Markov Chains. North Holland, New York. | Zbl

Touati (1988). Théorèmes limites pour les processus de Markov récurrents. To appear in Prob. Theory and Rel. Fields. | Zbl

Ueno, T. (1960). On recurrent Markov processes. Kodai Math. Sens. Rep. 12, 109-142. | Zbl | DOI