2024/08/22 by Alexandra Blessing, Alex Blumenthal, Blessing, Alexandra +5 · 1 citation
Economics, Econometrics and Finance · #37H15 #37H20 #60F10 #68V99 #Dynamical Systems (math.DS) #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2408.12556
openalex publication_date 2024/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The main goal of this work is to provide a description of transitions from uniform to non-uniform snychronization in diffusions based on large deviation estimates for finite time Lyapunov exponents. These can be characterized in terms of moment Lyapunov exponents which are principal eigenvalues of the generator of the tilted (Feynman-Kac) semigroup. Using a computer assisted proof, we demonstrate how to determine these eigenvalues and investigate the rate function which is the Legendre-Fenichel transform of the moment Lyapunov function. We apply our results to two case studies: the pitchfork bifurcation and a two-dimensional toy model, also considering the transition to a positive asymptotic Lyapunov exponent.