An extension of P. Lévy's distributional
Erik Graversen, Svend ; Shiryaev, Albert N.
Bernoulli, Tome 6 (2000) no. 6, p. 615-620 / Harvested from Project Euclid
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We extend the well-known P. Lévy theorem on the distributional identity $(M_t-B_t,M_t)\simeq(|B_t|,L(B)_t)$ , where $(B_t)$ is a standard Brownian motion and $(M_t)=(sup_{0\leq s \leq t}B_s)$ to the case of Brownian motion with drift λ. Processes of the type ¶ $$ \d X_t^\lambda =-\lambda\,\sgn(X_t^\lambda )\d t+\d B_t $$ ¶ appear naturally in the generalization.
Publié le : 2000-08-14
Classification:  Brownian motion,  local time,  Markov processes 
@article{1081449596,
     author = {Erik Graversen, Svend and Shiryaev, Albert N.},
     title = {An extension of P. L\'evy's distributional},
     journal = {Bernoulli},
     volume = {6},
     number = {6},
     year = {2000},
     pages = { 615-620},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1081449596}
}

Erik Graversen, Svend; Shiryaev, Albert N. An extension of P. Lévy's distributional. Bernoulli, Tome 6 (2000) no. 6, pp.  615-620. http://gdmltest.u-ga.fr/item/1081449596/