Temps locaux d'intersection et points multiples des processus de Lévy

Le Gall, Jean-François

Séminaire de probabilités de Strasbourg, Tome 21 (1987), p. 341-374 / Harvested from Numdam

Détail

Publié le : 1987-01-01

MR 941994 | Zbl 0621.60077

Bibliographie

[1] Aizenman, M.Communication personnelle.

[2] Blumenthal, R.M. ; Getoor, R.K. Markov processes and potentiàl theory. Academic Press, New-York, 1968. | MR 264757 | Zbl 0169.49204

[3] Dvoretzky, A. ; Erdös, P. Some problems on random walk in space. Proc. Second Berkeley Symp. on Math. Statistics and Probability. University of California Press, Berkeley, 1951, p. 353-367. | MR 47272 | Zbl 0044.14001

[4] Dynkin, E.B. Additive functionals of several time-reversible Markov processes. J. Funct. Anal. 42 (1981), 64-101. | MR 620580 | Zbl 0467.60069

[5] Dynkin, E.B. Random fields associated with multiple points of the Brownian motion. J. Funct. Anal. 62 (1985), 397-434. | MR 794777 | Zbl 0579.60081

[6] Dynkin, E.B. Self-intersection gauge for random walks and for Brownian motion. A paraître dans Ann. Probab. (1987). | MR 920254 | Zbl 0638.60081

[7] Evans, S.N. Potential theory for a family of several Markov processes. A paraître aux Ann. Inst. Henri Poincaré (1987). | Numdam | MR 906728 | Zbl 0625.60086

[8] Geman, D. ; Horowitz, J. ; Rosen, J. A local time analysis of intersections of Brownian paths in the plane. Ann. Probab. 12 (1984), 86-107. | MR 723731 | Zbl 0536.60046

[9] Hawkes, J. Potential theory of Lévy processes. Proc. London Math. Soc. (3) (1979), 335-352. | MR 531166 | Zbl 0401.60069

[10] Hawkes, J.. Multiple points for symmetric Lévy processes. Math. Proc. Cambridge Philos. Soc. 83 (1978), 83-90. | MR 464385 | Zbl 0396.60067

[11] Ito, K. ; Mc Kean, H.P.Diffusion processes and their sample paths. Second Printing. Springer - Verlag, Berlin, 1974. | MR 345224 | Zbl 0285.60063

[12] Kesten, H. Hitting probabilities of single points for processes with stationary independent increments. Mem. Amer. Math. Soc. 93 (1969). | MR 272059 | Zbl 0186.50202

[13] Le Gall, J.F.,Sur la mesure de Hausdorff de la courbe brownienne. Séminaire de Probabilités XIX. Lect. Notes in Math. 1123. Springer - Verlag, Berlin, 1985, p. 297-313. | Numdam | MR 889491 | Zbl 0563.60071

[14] Le Gall, J.F.Sur la saucisse de Wiener et les points multiples du mouvement brownien. Ann. Probab. 14 (1986). | MR 866344 | Zbl 0621.60083

[15] Le Gall, J.F.Propriétés d'intersection des marches aléatoires, I. Comm. Math. Phys. 104 (1986), 471-507. | MR 840748 | Zbl 0609.60078

[16] Le Gall, J.F. Le comportement du mouvement brownien entre les deux instants où il passe par un point double. J. Funct. Anal. 70 (1987). | MR 880979 | Zbl 0624.60090

[17] Le Gall, J.F.The exact Hausdorff measure of Brownian multiple points. A paraître dans le Seminar on Stochastic Processes 1986. Birkhäuser. | Zbl 0619.60073

[18] Le Gall, J.F.Fluctuation results for the Wiener sausage. Preprint (1986), soumis à Ann. Probab. | MR 942751 | Zbl 0665.60080

[19] Le Gall, J.F. ; Rosen, J. ;Shieh, N.R.Multiple pointsfor Lévy processes. Preprint (1986).

[20] Le Gall, J.F. ; Rosen, J.Limit theorems for random walks in the domain of attraction of a stable law. Article en préparation.

[21] Le Gall, J.F. ; Taylor, S.J.The packing measure of planar Brownian motion. A paraître dans le Seminar on Stochastic Processes 1986. Birkhäuser. | Zbl 0619.60074

[22] Neveu, J. Bases mathématiques du calcul des probabilités. Masson, Paris 1970. | MR 272004 | Zbl 0203.49901

[23] Ray, D.Sojourn times and the exact Hausdorff measure of the sample path for planar Brownian motion. Trans. Amer. Math. Soc. 106 (1963),436-444. | MR 145599 | Zbl 0119.14602

[24] Rogers, C.A. ; Taylor, S.J. Functions continuous and sinpular with respect to a Hausdorff measure. Mathematika 8 (1961), 1-31. | MR 130336 | Zbl 0145.28701

[25] Rosen, J. A local time approach to the self-intersections of Brownian paths in space. Comm. Math. Phys. 88 (1983), 327-338. | MR 701921 | Zbl 0534.60070

[26] Rosen, J. Joint continuity of the intersection local times of Markov processes. A paraître dans Ann. Probab. (1987). | MR 885136 | Zbl 0622.60084

[27] Rosen, J. Continuity and singularity of the intersection local time of stable processes in R2. Preprint (1985). | MR 920256

[28] Sznitman, A.S. Some bounds and limiting results for the measure of Wiener sausage of small radius associated to elliptic diffusions. Preprint (1986). | MR 904262

[29] Taylor, S.J. Multiple points for the sample paths of the symmetric stable process. Z. Wahrsch. verw. Gebiete 5 (1966), 247-264. | MR 202193 | Zbl 0146.37905

[30] Taylor, S.J. Sample path properties of a transient stable process. J. Math. Mech. 16 (1967), 1229-1246. | MR 208684 | Zbl 0178.19301

[31] Taylor, S.J. The measure theory of random fractals. Math. Proc. Cambridge Philos. Soc. 100 (1986), 383-406. | MR 857718 | Zbl 0622.60021

[32] Taylor, S.J. ; Tricot, C. Packing measure and its evaluation for a Brownian path. Trans. Amer. Math. Soc. 288 (1985), 679-699. | MR 776398 | Zbl 0537.28003

[33] Williams, D. Path decomposition and continuity of local time for one-dimensional diffusions, I. Proc. London Math. Soc (3) 28 (1974), 738-768. | MR 350881 | Zbl 0326.60093

[34] Wolpert, R. Wiener path intersections and local time. J. Funct. Anal. 30 (1978), 329-340. | MR 518339 | Zbl 0403.60069

[35] Yor, M.Précisions sur l'existence et la continuité des temps locaux d'intersection du mouvement brownien dans Rd. Séminaire de Probabilités XX. Lect. Notes in Math. 1204. Springer - Verlag, Berlin, 1986, p. 532-542. | Numdam | MR 942042 | Zbl 0611.60066