Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations
| dc.contributor.author | Bakhtin, Y | |
| dc.contributor.author | Mattingly, JC | |
| dc.date.accessioned | 2022-04-01T14:02:07Z | |
| dc.date.available | 2022-04-01T14:02:07Z | |
| dc.date.issued | 2005-10-01 | |
| dc.date.updated | 2022-04-01T14:02:06Z | |
| dc.description.abstract | We explore Itô stochastic differential equations where the drift term possibly depends on the infinite past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proven if the dependence on the past decays sufficiently fast. The results of this paper are then applied to stochastically forced dissipative partial differential equations such as the stochastic Navier-Stokes equation and stochastic Ginsburg-Landau equation. © World Scientific Publishing Company. | |
| dc.identifier.issn | 0219-1997 | |
| dc.identifier.issn | 1793-6683 | |
| dc.identifier.uri | ||
| dc.language | en | |
| dc.publisher | World Scientific Pub Co Pte Lt | |
| dc.relation.ispartof | Communications in Contemporary Mathematics | |
| dc.relation.isversionof | 10.1142/S0219199705001878 | |
| dc.subject | Science & Technology | |
| dc.subject | Physical Sciences | |
| dc.subject | Mathematics, Applied | |
| dc.subject | Mathematics | |
| dc.subject | stochastic differential equations | |
| dc.subject | memory | |
| dc.subject | Lyapunov functions | |
| dc.subject | ergodicity | |
| dc.subject | stationary solutions | |
| dc.subject | stochastic Navier-Stokes equation | |
| dc.subject | stochastic Ginsburg-Landau equation | |
| dc.subject | NAVIER-STOKES EQUATIONS | |
| dc.subject | FORCED NONLINEAR PDES | |
| dc.subject | COUPLING APPROACH | |
| dc.subject | ERGODICITY | |
| dc.subject | DYNAMICS | |
| dc.title | Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations | |
| dc.type | Journal article | |
| duke.contributor.orcid | Mattingly, JC|0000-0002-1819-729X | |
| pubs.begin-page | 553 | |
| pubs.end-page | 582 | |
| pubs.issue | 5 | |
| pubs.organisational-group | Duke | |
| pubs.organisational-group | Trinity College of Arts & Sciences | |
| pubs.organisational-group | Mathematics | |
| pubs.organisational-group | Statistical Science | |
| pubs.publication-status | Published | |
| pubs.volume | 7 |