tailieunhanh - Báo cáo hóa học: " Necessary and sufficient condition for the smoothness of intersection local time of subfractional Brownian motions Guangjun Shen"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Necessary and sufficient condition for the smoothness of intersection local time of subfractional Brownian motions Guangjun Shen | Shen Journal of Inequalities and Applications 2011 2011 139 http content 2011 1 139 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Necessary and sufficient condition for the smoothness of intersection local time of subfractional Brownian motions Guangjun Shen Correspondence guangjunshen@ Department of Mathematics Anhui Normal University Wuhu 241000 China Abstract Let SH and sH be two independent d-dimensional sub-fractional Brownian motions with indices H e 0 1 . Assume d 2 we investigate the intersection local time of subfractional Brownian T T t s sH 0 0 motions sH dsdí T 0 - where Ỗ denotes the Dirac delta function at zero. By elementary inequalities we show that lT exists in L2 if and only if Hd 2 and it is smooth in the sense of the Meyer-Watanabe if and only if H d 2. As a related problem we give also the regularity of the intersection local time process. 2010 Mathematics Subject Classification 60G15 60F25 60G18 60J55. Keywords subfractional Brownian motion intersection local time Chaos expansion 1. Introduction The intersection properties of Brownian motion paths have been investigated since the forties see 1 and since then a large number of results on intersection local times of Brownian motion have been accumulated see Wolpert 2 Geman et al. 3 Imkeller et al. 4 de Faria et al. 5 Albeverio et al. 6 and the references therein . The intersection local time of independent fractional Brownian motions has been studied by Chen and Yan 7 Nualart et al. 8 Rosen 9 Wu and Xiao 10 and the references therein. As for applications in physics the Edwards model of long polymer molecules by Brownian motion paths uses the intersection local time to model the excluded volume effect different parts of the molecule should not be located at the same point in space while Symanzik 11 Wolpert 12 introduced the intersection local time as a tool in constructive quantum field theory. .