We study the solution $\xi_t$ to an elliptic stochastic equation and the solution $(\xi_t, \eta_t)$ to a lift of this equation, under a condition on the behaviour of $\xi_t$. We obtain a "conditional" equation which gives the conditional behaviour, and we use it to deduce a conditioned version of the Stroock-Varadhan support theorem.
Publié le : 1988-10-14
Classification:
Stochastic equation,
conditional probability,
lift,
product space,
Stroock-Varadhan support theorem,
Doob $h$-transform,
60H10
@article{1176991601,
author = {Carverhill, Andrew},
title = {Conditioning a Lifted Stochastic System in a Product Space},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 1840-1853},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991601}
}
Carverhill, Andrew. Conditioning a Lifted Stochastic System in a Product Space. Ann. Probab., Tome 16 (1988) no. 4, pp. 1840-1853. http://gdmltest.u-ga.fr/item/1176991601/