A comparison theorem is proved for one-dimensional stochastic equations driven by continuous semimartingales and having Volterra-type drifts. A counterexample which shows that the coefficient of the continuous martingale term cannot be Volterra-type is given. Then the comparison result is used in order to obtain the existence of strong solutions when the Lipschitz condition is replaced by a Holder-type one.
Publié le : 1989-10-14
Classification:
Stochastic integral equations,
strong solutions,
Volterra drifts,
60H20
@article{1176991173,
author = {Tudor, Constantin},
title = {A Comparison Theorem for Stochastic Equations with Volterra Drifts},
journal = {Ann. Probab.},
volume = {17},
number = {4},
year = {1989},
pages = { 1541-1545},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991173}
}
Tudor, Constantin. A Comparison Theorem for Stochastic Equations with Volterra Drifts. Ann. Probab., Tome 17 (1989) no. 4, pp. 1541-1545. http://gdmltest.u-ga.fr/item/1176991173/