On définit plusieurs approximations du processus des temps locaux au niveau x du mouvement brownien réel . En particulier, on montre que et convergent au sens ucp vers , lorsque . D'autre part, on montre que converge vers dans et que la vitesse de convergence est d'ordre , pour tout .
We give some approximations of the local time process at level x of the real Brownian motion . We prove that and converge in the ucp sense to , as . We show that goes to in as , and that the rate of convergence is of order , for any .
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@article{CRMATH_2007__345_1_45_0, author = {Bergery, Blandine B\'erard and Vallois, Pierre}, title = {Quelques approximations du temps local brownien}, journal = {Comptes Rendus. Math\'ematique}, pages = {45--48}, publisher = {Elsevier}, volume = {345}, number = {1}, year = {2007}, doi = {10.1016/j.crma.2007.05.007}, language = {fr}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.05.007/} }
TY - JOUR AU - Bergery, Blandine Bérard AU - Vallois, Pierre TI - Quelques approximations du temps local brownien JO - Comptes Rendus. Mathématique PY - 2007 SP - 45 EP - 48 VL - 345 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.05.007/ DO - 10.1016/j.crma.2007.05.007 LA - fr ID - CRMATH_2007__345_1_45_0 ER -
%0 Journal Article %A Bergery, Blandine Bérard %A Vallois, Pierre %T Quelques approximations du temps local brownien %J Comptes Rendus. Mathématique %D 2007 %P 45-48 %V 345 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.05.007/ %R 10.1016/j.crma.2007.05.007 %G fr %F CRMATH_2007__345_1_45_0
Bergery, Blandine Bérard; Vallois, Pierre. Quelques approximations du temps local brownien. Comptes Rendus. Mathématique, Tome 345 (2007) no. 1, pp. 45-48. doi : 10.1016/j.crma.2007.05.007. http://archive.numdam.org/articles/10.1016/j.crma.2007.05.007/
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