A Stopped Brownian Motion Formula
Taylor, Howard M.
Ann. Probab., Tome 3 (1975) no. 6, p. 234-246 / Harvested from Project Euclid
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We determine $E\lbrack \exp (\alpha X(T) - \beta T) \rbrack$ where $X(t)$ is a Brownian motion having arbitrary drift and variance and $T$ is the first time the process drops a specified amount below its maximum to date. From this result, the moments of $X(T)$ and $T$ and some asymptotic distributions may be found. Applications in process control and financial management are mentioned.
Publié le : 1975-04-14
Classification:  60,  J65,  Moment generating function,  Brownian motion,  stopping time 
@article{1176996395,
     author = {Taylor, Howard M.},
     title = {A Stopped Brownian Motion Formula},
     journal = {Ann. Probab.},
     volume = {3},
     number = {6},
     year = {1975},
     pages = { 234-246},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996395}
}

Taylor, Howard M. A Stopped Brownian Motion Formula. Ann. Probab., Tome 3 (1975) no. 6, pp.  234-246. http://gdmltest.u-ga.fr/item/1176996395/