Taylor expansions of curve-crossing probabilities

被引：4

作者：

Hobson, DG ^{[1
]}

Williams, D ^{[1
]}

Wood, ATA ^{[1
]}

机构：

[1] Univ Bath, Bath BA2 7AY, Avon, England

来源：

BERNOULLI | 1999年 / 5卷 / 05期

关键词：

Brownian motion; Cameron-Martin-Girsanov theorem; curve-crossing probabilities; harmonic functions; Levy-Khinchine operator;

D O I：

10.2307/3318444

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Using an approach based on the Cameron-Martin-Girsanov theorem, we obtain a Taylor expansion for the probability that Brownian motion hits a smooth nonlinear boundary which grows at a suitable rate. The structure and probabilistic meaning of the terms in the expansion are studied in some detail.

引用

收藏

页码：779 / 795

页数：17

相关论文

共 13 条

[1] SEQUENTIAL-TESTS CONSTRUCTED FROM IMAGES [J].

DANIELS, HE .

ANNALS OF STATISTICS, 1982, 10 (02) :394-400

[2]

DANIELS HE, 1996, BERNOULLI, V2, P133

[3] THE 1ST-PASSAGE DENSITY OF A CONTINUOUS GAUSSIAN PROCESS TO A GENERAL BOUNDARY [J].

DURBIN, J .

JOURNAL OF APPLIED PROBABILITY, 1985, 22 (01) :99-122

[4] A RECONCILIATION OF 2 DIFFERENT EXPRESSIONS FOR THE 1ST-PASSAGE DENSITY OF BROWNIAN-MOTION TO A CURVED BOUNDARY [J].

DURBIN, J .

JOURNAL OF APPLIED PROBABILITY, 1988, 25 (04) :829-832

[5] THE 1ST-PASSAGE DENSITY OF THE BROWNIAN-MOTION PROCESS TO A CURVED BOUNDARY [J].

DURBIN, J ;

WILLIAMS, D .

JOURNAL OF APPLIED PROBABILITY, 1992, 29 (02) :291-304

[6] ASYMPTOTIC EXPANSIONS IN FUNCTIONAL LIMIT-THEOREMS [J].

GOTZE, F .

JOURNAL OF MULTIVARIATE ANALYSIS, 1985, 16 (01) :1-20

[7]

Karatzas I., 1998, GRADUATE TEXTS MATH, V113

[8]

Lerche H. R., 1986, LECT NOTES STAT, V40

[9]

Revuz D., 2013, Continuous martingales and Brownian motion, V293

[10] BOUNDARY CROSSING PROBABILITIES FOR WIENER PROCESS AND SAMPLE SUMS [J].

ROBBINS, H ;

SIEGMUND, D .

ANNALS OF MATHEMATICAL STATISTICS, 1970, 41 (05) :1410-&