Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds

Lubomir Banas; Zdzislaw Brzezniak; Martin Ondreját; Andreas Prohl

Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds

Lubomir Banas, Zdzislaw Brzezniak, Martin Ondreját, Andreas Prohl

Mathematics

Research output: Working paper › Preprint

Abstract

We give a sufficient condition on nonlinearities of an SDE on a compact connected Riemannian manifold $M$ which implies that laws of all solutions converge weakly to the normalized Riemannian volume measure on $M$. This result is further applied to characterize invariant and ergodic measures for various SDEs on manifolds.

Original language	English
Number of pages	17
Publication status	Published - Feb 2011

Access to Document

http://arxiv.org/abs/1102.0728

Cite this

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title = "Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds",

abstract = "We give a sufficient condition on nonlinearities of an SDE on a compact connected Riemannian manifold $M$ which implies that laws of all solutions converge weakly to the normalized Riemannian volume measure on $M$. This result is further applied to characterize invariant and ergodic measures for various SDEs on manifolds. ",

author = "Lubomir Banas and Zdzislaw Brzezniak and Martin Ondrej{\'a}t and Andreas Prohl",

year = "2011",

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AU - Banas, Lubomir

AU - Brzezniak, Zdzislaw

AU - Ondreját, Martin

AU - Prohl, Andreas

PY - 2011/2

Y1 - 2011/2

N2 - We give a sufficient condition on nonlinearities of an SDE on a compact connected Riemannian manifold $M$ which implies that laws of all solutions converge weakly to the normalized Riemannian volume measure on $M$. This result is further applied to characterize invariant and ergodic measures for various SDEs on manifolds.

AB - We give a sufficient condition on nonlinearities of an SDE on a compact connected Riemannian manifold $M$ which implies that laws of all solutions converge weakly to the normalized Riemannian volume measure on $M$. This result is further applied to characterize invariant and ergodic measures for various SDEs on manifolds.

M3 - Preprint

BT - Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds

ER -