Solow system driven by $α$-stable Lévy process

What the math gives to ML

The paper's transferable mechanism is an Ornstein–Uhlenbeck-like mean-reverting state driven by symmetric alpha-stable Lévy jumps, producing discontinuous heavy-tailed fluctuations with infinite variance while retaining an analytically characterized stationary law. The key asset for neural networks is a jump-noise optimizer or parameter perturbation process whose restoring drift gives a quantitative contraction condition, while alpha-stable shocks enable occasional large basin escapes without relying on Gaussian variance estimates. A practical transfer is to add a mean-reverting parameter-anchor drift and symmetric stable jumps to SGD, and test both the predicted contraction boundary and the stationary characteristic function before measuring task performance.