Details

Autor(en) / Beteiligte

• Benaïm, Michel
• Gauthier, Carl-Erik

Titel

Self-repelling diffusions on a Riemannian manifold

Ist Teil von

• Probability theory and related fields, 2017-10, Vol.169 (1-2), p.63-104

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2017

Link zum Volltext

Quelle

Business Source Ultimate

Beschreibungen/Notizen

• Let M be a compact connected oriented Riemannian manifold. The purpose of this paper is to investigate the long time behavior of a degenerate stochastic differential equation on the state space M × R n ; which is obtained via a natural change of variable from a self-repelling diffusion taking the form d X t = σ d B t ( X t ) - ∫ 0 t ∇ V X s ( X t ) d s d t , X 0 = x where { B t } is a Brownian vector field on M , σ > 0 and V x ( y ) = V ( x , y ) is a diagonal Mercer kernel. We prove that the induced semi-group enjoys the strong Feller property and has a unique invariant probability μ given as the product of the normalized Riemannian measure on M and a Gaussian measure on R n . We then prove an exponential decay to this invariant probability in L 2 ( μ ) and in total variation.