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Distribution of the Brownian motion on its way to hitting zero

  
@article{ECP1432,
	author = {Pavel Chigansky and Fima Klebaner},
	title = {Distribution of the Brownian motion on its way to hitting zero},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {Brownian motion; hitting time; heavy-tailed distribution; scaled Brownian excursion; Bessel bridge; Brownian bridge},
	abstract = {For the one-dimensional Brownian motion $B=(B_t)_{t\geq 0}$, started at $x>0$, and theĀ  first hitting time $\tau=\inf\{t\geq 0:B_t=0\}$, we find the probability density of $B_{u\tau}$ for a $u\in(0,1)$, i.e. of the Brownian motion on its way to hitting zero.},
	pages = {no. 58, 641-648},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1432},    
        url = {http://ecp.ejpecp.org/article/view/1432}}