On the invariant measure of a positive recurrent diffusion in R

dc.creatorBaldini, Michele L.
dc.date2004-12-20
dc.date.accessioned2026-07-07T05:15:30Z
dc.date.available2026-07-07T05:15:30Z
dc.descriptionGiven 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.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0412410
dc.identifierhttp://arxiv.org/abs/math/0412410
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73651
dc.subjectProbability
dc.subject60J60, 60H15
dc.titleOn the invariant measure of a positive recurrent diffusion in R
dc.typetext

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