A new method is described for constructing a generalized solution of a stochastic evolution equation. Existence, uniqueness, regularity and a probabilistic representation of this Wiener Chaos solution are established for a large class of equations. As an application of the general theory, new results are obtained for several types of the passive scalar equation.
Publié le : 2006-03-14
Classification:
Feynmann–Kac formula,
generalized random elements,
stochastic parabolic equations,
turbulent transport,
white noise,
60H15,
35R60,
60H40
@article{1147179985,
author = {Lototsky, S. V. and Rozovskii, B. L.},
title = {Wiener chaos solutions of linear stochastic evolution equations},
journal = {Ann. Probab.},
volume = {34},
number = {1},
year = {2006},
pages = { 638-662},
language = {en},
url = {http://dml.mathdoc.fr/item/1147179985}
}
Lototsky, S. V.; Rozovskii, B. L. Wiener chaos solutions of linear stochastic evolution equations. Ann. Probab., Tome 34 (2006) no. 1, pp. 638-662. http://gdmltest.u-ga.fr/item/1147179985/