SMEARING DISTRIBUTIONS AND THEIR USE IN FINANCIAL MARKETS

It is shown that superpositions of path integrals with arbitrary Hamiltonians and different scaling parameters υ ("variances") obey the Chapman-Kolmogorov relation for Markovian processes if and only if the corresponding smearing distributions for υ have a specific functional form. Ensuing "smearing" distributions substantially simplify the coupled system of Fokker-Planck equations for smeared and unsmeared conditional probabilities. Simple application in financial models with stochastic volatility is presented.