Some Potential Theory for Reflecting Brownian Motion in Holder and Lipschitz Domains
Bass, Richard F. ; Hsu, Pei
Ann. Probab., Tome 19 (1991) no. 4, p. 486-508 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
Bounds are found on the transition densities and Green functions for Brownian motion with normal reflection in Holder and Lipschitz domains. For Lipschitz domains, reflecting Brownian motion and boundary local time are constructed, a Harnack inequality valid up to the boundary is proved, a probabilistic solution to the Neumann problem is given and the Kuramochi boundary is identified.
Publié le : 1991-04-14
Classification:  Reflecting Brownian motion,  Lipschitz domain,  Holder domain,  Kuramochi boundary,  transition density,  Green function,  Neumann problem,  60J65,  60J35,  60J50 
@article{1176990437,
     author = {Bass, Richard F. and Hsu, Pei},
     title = {Some Potential Theory for Reflecting Brownian Motion in Holder and Lipschitz Domains},
     journal = {Ann. Probab.},
     volume = {19},
     number = {4},
     year = {1991},
     pages = { 486-508},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176990437}
}

Bass, Richard F.; Hsu, Pei. Some Potential Theory for Reflecting Brownian Motion in Holder and Lipschitz Domains. Ann. Probab., Tome 19 (1991) no. 4, pp.  486-508. http://gdmltest.u-ga.fr/item/1176990437/