We obtain a diffusion approximation result for processes satisfying equations with past-dependent coefficients. We apply this result to a model of option pricing, in which the underlying asset price volatility depends on past evolution, and obtain a generalized (asymptotic) Black and Scholes formula.
"Diffusion Approximation in Past Dependent Models and Applications to Option Pricing." Ann. Appl. Probab. 1 (3) 379 - 405, August, 1991. https://doi.org/10.1214/aoap/1177005873