XVII: 02, 15-31, LNM 986 (1983)
LE GALL, Jean-François
Applications du temps local aux équations différentielles stochastiques unidimensionnelles
Retrieve article from Numdam
XVII: 08, 81-88, LNM 986 (1983)
LE GALL, Jean-François;
YOR, Marc
Sur l'équation stochastique de Tsirelson Retrieve article from Numdam
XIX: 27, 297-313, LNM 1123 (1985)
LE GALL, Jean-François
Sur la mesure de Hausdorff de la courbe brownienne (
Brownian motion)
Previous results on the $h$-measure of the Brownian curve in $
R^2$ or $
R^3$ indexed by $t\in[0,1]$, by Cisielski-Taylor
Trans. Amer. Math. Soc. 103 (1962) and Taylor
Proc. Cambridge Philos. Soc. 60 (1964) are sharpened. The method uses the description à la Ray-Knight of the local times of Bessel processes
Comment: These Ray-Knight descriptions are useful ; they were later used in questions not related to Hausdorff measures. See for instance Biane-Yor,
Ann. I.H.P. 23 (1987), Yor,
Ann. I.H.P. 27 (1991)
Keywords: Hausdorff measures,
Brownian motion,
Bessel processes,
Ray-Knight theoremsNature: Original Retrieve article from Numdam
XIX: 28, 314-331, LNM 1123 (1985)
LE GALL, Jean-François
Sur le temps local d'intersection du mouvement brownien plan et la méthode de renormalisation de Varadhan (
Brownian motion)
The normalized self-intersection local time of planar Brownian motion was shown to exist by Varadhan (Appendix to
Euclidean quantum field theory, by K.~Symanzik, in
Local Quantum Theory, Academic Press, 1969). This is established anew here by a completely different method, using the intersection local time of two independent planar Brownian motions (whose existence was established by Geman, Horowitz and Rosen,
Ann. Prob. 12, 1984) and a sequence of dyadic decompositions of the triangle $\{0<s<t\le1\}$
Comment: Later, Dynkin, Rosen, Le Gall and others have shown existence of a renormalized local time for the multiple self-intersection of arbitrary order $n$ of planar Brownian motion. A good reference is Le Gall,
École d'Été de Saint-Flour XX, Springer LNM 1527
Keywords: Brownian motion,
Local times,
Self-intersectionNature: Original proofs Retrieve article from Numdam
XX: 30, 447-464, LNM 1204 (1986)
LE GALL, Jean-François
Une approche élémentaire des théorèmes de décomposition de Williams Retrieve article from Numdam
XXI: 18, 270-275, LNM 1247 (1987)
BIANE, Philippe;
LE GALL, Jean-François;
YOR, Marc
Un processus qui ressemble au pont brownien Retrieve article from Numdam
XXI: 22, 341-374, LNM 1247 (1987)
LE GALL, Jean-François
Temps locaux d'intersection et points multiples des processus de Lévy Retrieve article from Numdam
XXII: 19, 186-189, LNM 1321 (1988)
LE GALL, Jean-François
Sur les fonctions polaires pour le mouvement brownien Retrieve article from Numdam
XXIII: 22, 258-274, LNM 1372 (1989)
LE GALL, Jean-François
Marches aléatoires, mouvement brownien et processus de branchement Retrieve article from Numdam
XXVIII: 16, 172-180, LNM 1583 (1994)
LE GALL, Jean-François
Exponential moments for the renormalized self-intersection local time of planar Brownian motion Retrieve article from Numdam
XXXI: 11, 103-112, LNM 1655 (1997)
LE GALL, Jean-François
Marches aléatoires auto-évitantes et mesures de polymères Retrieve article from Numdam
XLVII: 07, 89-105, LNM 2137 (2015)
LE GALL, Jean-François
Bessel Processes, the Brownian Snake and Super-Brownian MotionNature: Original
