The asymptotic behavior of fraudulent algorithms
Abstract
Let U be a Morse function on a compact connected m-dimensional Riemannian manifold, m≥2, satisfying minU=0 and let U={x∈M:U(x)=0} be the set of global minimizers. Consider the stochastic algorithm X(β):=(X(β)(t))t≥0 taking values in M, whose generator is U△[·]−β⟨∇U,∇[·]⟩, where β∈R is a real parameter. We show that for β>m2−1, X(β)(t) converges a.s. as t→∞, toward a point p∈U and that each p∈U has a positive probability to be selected when X(β)(0)∉U. On the other hand, for β
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Topological and Geometric Data Analysis
Markov Chains and Monte Carlo Methods
Publication details
- Journal / source
- The Annals of Applied Probability
- Volume
- 36
- Issue
- 3
- Publication date
- 1 June 2026
- Language
- EN