Intersection local times as generalized white noise functionals

被引:22
作者
DeFaria, M
Hida, T
Streit, L
Watanabe, H
机构
[1] UNIV BIELEFELD, BIBOS, D-33501 BIELEFELD, GERMANY
[2] OKAYAMA UNIV SCI, OKAYAMA 700, JAPAN
关键词
Brownian motion; local time; white noise analysis;
D O I
10.1023/A:1005782030567
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
For any dimension we present the expansions of Brownian motion self-intersection local times in terms of multiple Wiener integrals. Suitably subtracted, they exist in the sense of generalized white noise functionals; their kernel functions are given in closed (and remarkably simple) form.
引用
收藏
页码:351 / 362
页数:12
相关论文
共 34 条
[1]  
[Anonymous], LECT NOTES MATH
[2]  
[Anonymous], 1957, P CAMB PHILOS SOC, DOI DOI 10.1017/S0305004100032989
[3]  
[Anonymous], LOCAL QUANTUM THEORY
[4]  
BASS RF, 1993, ANN I H POINCARE-PR, V29, P419
[5]  
Dvoretzky A., 1954, B RESEARCH COUNCIL F, V3, P364
[6]  
Dvoretzky A., 1950, Acta Sci Math, V12, P75
[7]   SELF-INTERSECTION GAUGE FOR RANDOM-WALKS AND FOR BROWNIAN-MOTION [J].
DYNKIN, EB .
ANNALS OF PROBABILITY, 1988, 16 (01) :1-57
[8]   POLYNOMIALS OF THE OCCUPATION FIELD AND RELATED RANDOM-FIELDS [J].
DYNKIN, EB .
JOURNAL OF FUNCTIONAL ANALYSIS, 1984, 58 (01) :20-52
[9]   REGULARIZED SELF-INTERSECTION LOCAL-TIMES OF PLANAR BROWNIAN-MOTION [J].
DYNKIN, EB .
ANNALS OF PROBABILITY, 1988, 16 (01) :58-74
[10]   A LOCAL TIME ANALYSIS OF INTERSECTIONS OF BROWNIAN PATHS IN THE PLANE [J].
GEMAN, D ;
HOROWITZ, J ;
ROSEN, J .
ANNALS OF PROBABILITY, 1984, 12 (01) :86-107