✦ LIBER ✦
Some conditional crossing results of Brownian motion over a piecewise-linear boundary
✍ Scribed by Mario Abundo
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 150 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
✦ Synopsis
Explicit formulae are found for the probability that the Brownian motion, B t ; up-crosses, in [0; T ]; a piecewise-linear function S(t); with the condition that the value of B t is assigned at a future time u ¿ T or at an intermediate time u ¡ T . Also, the analogous conditional probability concerning |B t | is obtained. These results permit to obtain an explicit expression for the ÿrst-passage-time distribution function of the generalized Brownian bridge, over S(t).