Central Limit Theorem for one and two dimensional Self-Repelling Diffusions

Carl-Erik Gauthier
2018 Latin American Journal of Probability and Mathematical Statistics  
We prove a Central Limit Theorem for the finite dimensional distributions of the displacement for the 1-dimensional self-repelling diffusion which solves n k=1 a k cos(kx) with n < ∞ and a 1 , · · · , a n > 0. A 2-dimensional extension is also discussed. In dimension d ≥ 3, such a result has already been established by Horváth, Tóth and Vetö in 2012 for a large class of interaction functions F , but not for d = 1, 2. Under an integrability condition, Tarrès, Tóth and Valkó conjectured that a
more » ... njectured that a Central Limit Theorem result should also hold in dimension d = 1.
doi:10.30757/alea.v15-26 fatcat:pf3ujxruqjeupezup73seozgrm