Diffusing diffusivity selects Pareto tail exponent in random growth with redistribution (opens in new tab)

Random multiplicative growth with redistribution generates stationary Pareto wealth tails in the Bouchaud-M\'ezard model, but assumes a fixed multiplicative noise intensity. This is restrictive for physical and financial growth processes, where volatility (diffusivity) is often fluctuating. We replace the constant noise intensity by a diffusing diffusivity and ask how these fluctuations select the Pareto stationary tail. For a geometric Browni...