Papers

Write-ups grouped by example. The bibliography places them among the classical theory.

Regime switching

Cotton, P. (2001). An Analytic Approach to Ornstein–Uhlenbeck Processes with Fluctuating Parameters and Applications in the Modeling of Fixed Income Securities. PhD thesis, Stanford University. PDF · ProQuest. Vasicek's model with a mean and volatility driven by a fast secondary process, continuous or two-state, and the expansions that correct it.
Cotton, P. (2026). Survival Under Regime-Switching Ornstein–Uhlenbeck Hazard Rates: The Fast-Switching Expansion to All Orders. Note in preparation. Summary · certificates: verify_all_orders.py. The expansion in 1/λ to all orders, checked against a numerical solution of the two-state system.
Cotton, P. (2020). Got Milk? On Homogenization and Survival Probability. Article · code: homogenize. An expository account of the same model.

Cotton, P., Fouque, J.-P., Papanicolaou, G. and Sircar, R. (2004). Stochastic Volatility Corrections for Interest Rate Derivatives. Mathematical Finance 14, 173–200. doi:10.1111/j.0960-1627.2004.00188.x · PDF. Vasicek and CIR short rates with fast mean-reverting stochastic volatility, and the first-order terms that change the shape of the yield curve.
Fouque, J.-P., Papanicolaou, G. and Sircar, K. R. (2000). Derivatives in Financial Markets with Stochastic Volatility. Cambridge University Press. The fast-scale expansion for option prices.

Cotton, P. (2026). An Asymptotic Correction to Luce's Choice Axiom for Competing Correlated Cox Processes. Working draft: PDF. Softmax as the homogenized choice law of fast hidden kinetics, with its first correction.

Homogenization without the corrector, on conformalprediction.net. Residual pooling in split conformal prediction is the averaged limit, stopped before the corrector.

Homogenization, on skaters.microprediction.org. An online width adjustment for distributional forecasts built from a hedged two-point scale mixture.