On the invariant measure of a positive recurrent diffusion in R
| dc.creator | Baldini, Michele L. | |
| dc.date | 2004-12-20 | |
| dc.date.accessioned | 2026-07-07T05:15:30Z | |
| dc.date.available | 2026-07-07T05:15:30Z | |
| dc.description | Given an one-dimensional positive recurrent diffusion governed by the Stratonovich SDE \[ X_t=x+\int_0^tσ(X_s)\strat db(s)+\int_0^t m(X_s) ds, \] we show that the associated stochastic flow of diffeomorphisms focuses as fast as $ \mathrm{exp}(-2t\int_{R}\frac{m^2}{σ^2} dΠ)$, where $dΠ$ is the finite stationary measure. Moreover, if the drift is reversed and the diffeomorphism is inverted, then the path function so produced tends, independently of its starting point, to a single (random) point whose distribution is $dΠ$. Applications to stationary solutions of $X_t$, asymptotic behavior of solutions of SPDEs and random attractors are offered. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0412410 | |
| dc.identifier | http://arxiv.org/abs/math/0412410 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73651 | |
| dc.subject | Probability | |
| dc.subject | 60J60, 60H15 | |
| dc.title | On the invariant measure of a positive recurrent diffusion in R | |
| dc.type | text |