Stochastic bounds for Lévy processes
Doney, R. A.
Ann. Probab., Tome 32 (2004) no. 1A, p. 1545-1552 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
Using the Wiener–Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Lévy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Lévy process versions of many known results about the large-time behavior of random walks. This is illustrated by establishing a comprehensive theorem about Lévy processes which converge to ∞ in probability.
Publié le : 2004-04-14
Classification:  Processes with independent increments,  random walks,  exit times,  weak drift to infinity,  60G51,  60G17 
@article{1084884861,
     author = {Doney, R. A.},
     title = {Stochastic bounds for L\'evy processes},
     journal = {Ann. Probab.},
     volume = {32},
     number = {1A},
     year = {2004},
     pages = { 1545-1552},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1084884861}
}

Doney, R. A. Stochastic bounds for Lévy processes. Ann. Probab., Tome 32 (2004) no. 1A, pp.  1545-1552. http://gdmltest.u-ga.fr/item/1084884861/