Fractional Greenium Surfaces with Climate Memory

A fractional stochastic evolution is studied for the maturity-dependent spread between green and conventional forward rates. Its Caputo resolvent links the persistence of an initial greenium shock to the local scaling of subsequent fluctuations. The nonlinear equation is globally well posed for every finite probability moment exponent at least two under globally Lipschitz coefficients. In the Gaussian benchmark, covariance asymptotics hold in the trace norm, and so apply directly to the discontinuous maturity weights defining zero-coupon ratios. At positive observation times, the local variance contains a contribution from the reweighting of the entire preceding history. The resulting temporal exponent identifies the memory order, whereas identification of the maturity order depends on information about the noise covariance. These results give a statistical interpretation of climate memory effects without equating physical-measure exponential moments with arbitrage-free prices.