CHAOS EXPANSIONS OF DOUBLE INTERSECTION LOCAL TIME OF BROWNIAN-MOTION IN R(D) AND RENORMALIZATION

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:56

Article

IMKELLER, P ; PEREZABREU, V ; VIVES, J

关键词: BROWNIAN MOTION;    SELF INTERSECTIONS;    LOCAL TIME;    RENORMALIZATION;    MALLIAVINS CALCULUS;    MULTIPLE STOCHASTIC INTEGRALS;   

DOI  :  10.1016/0304-4149(94)00041-Q

来源: Elsevier

【 摘 要 】

Double intersection local times alpha(x,.) of Brownian motion W in R(d) which measure the size of the set of time pairs (s, t), s not equal t, for which W-t and W-s + x coincide can be developed into series of multiple Wiener-Ito integrals. These series representations reveal on the one hand the degree of smoothness of alpha(x,.) in terms of eventually negative order Sobolev spaces with respect to the canonical Dirichlet structure on Wiener space. On the other hand, they offer an easy access to renormalization of alpha(x,.) as \x\ --> 0. The results, valid for any dimension d, describe a pattern in which the well known cases d = 2, 3 are naturally embedded.

【 授权许可】

Free